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Sum & Difference of Angles
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Sum & Difference of Anglesy
x
1
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Sum & Difference of Anglesy
x
1
P
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Sum & Difference of Anglesy
x
1
P
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Sum & Difference of Anglesy
x
1
P
1
x
y
![Page 6: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/6.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
cos ,sin
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Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
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Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
![Page 9: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/9.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
![Page 10: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/10.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ
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Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
![Page 12: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/12.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
By coordinate geometry
![Page 13: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/13.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
2 22 cos cos sin sinPQ
By coordinate geometry
![Page 14: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/14.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
2 22 cos cos sin sinPQ 2 2 2 2 2cos 2cos cos cos sin 2sin sin sinPQ
By coordinate geometry
![Page 15: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/15.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
2 22 cos cos sin sinPQ 2 2 2 2 2cos 2cos cos cos sin 2sin sin sinPQ
By coordinate geometry
2 2 2cos cos 2sin sinPQ
![Page 16: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/16.jpg)
2 2cos 2 2cos cos 2sin sin
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2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
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2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
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2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
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2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
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2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
![Page 22: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/22.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin
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2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin
sinsincoscoscos
![Page 24: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/24.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 25: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/25.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 26: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/26.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 27: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/27.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 28: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/28.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 29: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/29.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
If it’s not the sine
sinsincoscoscos
![Page 30: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/30.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
If it’s not the sine,it’s not the sign
sinsincoscoscos
![Page 31: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/31.jpg)
Replace with 90
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Replace with 90
cos 90 cos 90 cos sin 90 sin
![Page 33: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/33.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
![Page 34: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/34.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
![Page 35: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/35.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with
![Page 36: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/36.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
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Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
![Page 38: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/38.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
![Page 39: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/39.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 40: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/40.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 41: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/41.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 42: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/42.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 43: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/43.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 44: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/44.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
If it’s the sine
![Page 45: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/45.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
If it’s the sine,it’s the sign
![Page 46: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/46.jpg)
tan
![Page 47: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/47.jpg)
tan
sin
tancos
![Page 48: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/48.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
![Page 49: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/49.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
![Page 50: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/50.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
![Page 51: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/51.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
Replace with
![Page 52: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/52.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
Replace with
tan tantan
1 tan tan
![Page 53: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/53.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
Replace with
tan tantan
1 tan tan
tan tan
(odd function i.e. )f x f x
![Page 54: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/54.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
Replace with
tan tantan
1 tan tan
tan tan
(odd function i.e. )f x f x tan tantan
1 tan tan
![Page 55: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/55.jpg)
tantan1tantantan
![Page 56: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/56.jpg)
tan plus tan
tantan1tantantan
![Page 57: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/57.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
![Page 58: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/58.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
Sum and Difference of Angles
![Page 59: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/59.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
Sum and Difference of Angles
sincoscossinsin
![Page 60: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/60.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
Sum and Difference of Angles
sincoscossinsin
sinsincoscoscos
![Page 61: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/61.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
Sum and Difference of Angles
sincoscossinsin
sinsincoscoscos
tantan1tantantan
![Page 62: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/62.jpg)
e.g. i Expand cos 2 3
![Page 63: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/63.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3
![Page 64: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/64.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
![Page 65: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/65.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
![Page 66: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/66.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
![Page 67: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/67.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
![Page 68: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/68.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
![Page 69: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/69.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
sin15 sin 45 30
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e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
sin15 sin 45 30
sin 45 cos30 cos 45 sin30
![Page 71: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/71.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
sin15 sin 45 30
sin 45 cos30 cos 45 sin30
1 3 1 12 22 2
![Page 72: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/72.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
sin15 sin 45 30
sin 45 cos30 cos 45 sin30
1 3 1 12 22 2
3 1
2 2
![Page 73: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/73.jpg)
2 1iv If sin and cos , find sin3 4
![Page 74: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/74.jpg)
2 1iv If sin and cos , find sin3 4
23
5
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2 1iv If sin and cos , find sin3 4
23
5
1
4 15
![Page 76: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/76.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
sin sin cos cos sin
![Page 77: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/77.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
sin sin cos cos sin
2 1 5 153 4 3 4
![Page 78: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/78.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
sin sin cos cos sin
2 1 5 153 4 3 4
2 5 3
12
![Page 79: 11 x1 t08 02 sum & difference of angles (2013)](https://reader033.vdocuments.net/reader033/viewer/2022042817/559f77761a28abbc418b4673/html5/thumbnails/79.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
sin sin cos cos sin
2 1 5 153 4 3 4
2 5 3
12
Exercise 14D; 1ade, 2bce, 5ac, 7, 9ac, 10ac, 12, 13ac, 16ab, 17, 23