trigo no

1

(1)

Verification of trigonometric identities

Fundamental Reciprocal identities sinx =1

cscx; cosx =

1

secx; tanx =

1

cotx

Ratio identities tanx =sinx

cosx; cotx =

cosx

sinx

Pythagorean identities sin2x+ cos2x = 1; 1 + cot2x = sec2x; tan2x+ 1 = csc2x.

1. Change to sines and cosins to verify an Identitysinx cotx secx = 1

2. Use pythagorean identity to verify an indentity1 2sin2x = 2cos2x 1

3. Factor to verify an indentitycsc2x cos2x csc2x = 1

4. Multiply by a conjugate to verify an identitysinx

1 + cosx=

1 cosxsinx

5. Change to sines and cosines to verify an indentitysinx+ tanx

1 + cosx= tanx

Exercises

1. tanx cscx cosx = 1 (1)

2. tanx secx sinx = tan2x (1)

3.4sin2x 12sinx+ 1

= 2sinx 1 (3)

4.sin2x 2sinx+ 1

sinx 1= sinx 1

5. (sinx cosx)(sinx+ cosx) = 1 2cos2x

6. (tanx)(1 cotx) = tanx 1

7.1

sinx 1

cosx=

cosx sinxsinx cosx

8.1

sinx+

1

cosx=

cosx+ 3sinx

sinx cosx

9.cosx

1 sinx= secx+ tanx

10.sinx

1 cosx= cscx+ cotx

11.1 tan4xsec2x

= 1 tan2x

12. sin4x cos4 = sin2x cos2x

13.1 tan3x1 + tanx

= 1 tanx+ tan2x

14.cosx tanx sinx

cotx= 0

15.sinx 2 + 1

sinx

sinx 1sinx

=sinx 1sinx+ 1