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Trigonometry - Trigonometric identities.
Test Yourself 2.


 

Simplify the following trigonometric identities:

Basic substitutions. 1.  
 

3.

 

4.Express the identity

in its simplest form.
  5.  
  7. 8.
Complementary angles.

9. Simplify:

cos (90o - θ) cosec (180o + θ)
Answer.-1

 10.Simplify .
Pythagorean relationships. 11.
Answer.0		 12.

 

 13. 14.

 

Prove the following trigonometric identities:

Basic substitutions
(change of defintion).		 15. Prove cosec A - sin A = cotA cos A. 16.
  17. 18. Prove
2tan2 α - 2tanα secα +1 = (secα - tanα )2
  19. Prove tan2x cos2x + cot2x sin2x = 1 20.
Pythagorean relationships.

21.

22. tan x - tan x sin2 x = sin x cos x
  23. 2 sec2α - 3 = 2 tan2α - 1 24.
  25. 26.
  27. 28.
  29. 30.
Mixed relationships. 31.  
  33.