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5.3 Sum and Difference Identities
Four very useful trig identities that we MUST know:
cos(A±B)=
sin(A±B)=
NOTE the sign change on the cosine identity.
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Ex. 1Find the value of cos(105o).
Ex. 2Find the value of cos(225o).
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Ex. 3Prove sin(π-x)=sinx
Ex. 4Rewrite as the sine or cosine of an angle
a) sin25ocos5o + cos25osin50
b) sin3xsin5x cos3xcos5x
c)
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Tangent sums and differencesOne pair of formulae for the sum or difference of tangent would be
tan(A±B)=
Another formula is:
tan(A+B)=
tan(A-B)=
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Ex. 6Prove
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Ex. 7Solve cosxsin2x+cos2xsinx=0.
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Ex. 8Express 2sinx+5cosx as a sinusoid in the form f(x)=asin(bx+c).