Trigonometric Identity Proofs Worksheet
Prove trigonometric identities using fundamental identities, algebraic manipulation, and various proof techniques.
Includes
Standards
Topics
Trigonometric Identity Proofs
Name:
Date:
Score:
Prove the following trigonometric identities. Show all your steps clearly. Use fundamental identities, algebraic manipulation, and any other valid proof techniques.
1. Prove the identity: (sin θ + cos θ)² = 1 + 2sin θ cos θ
2. Complete the steps to prove the identity: tan x + cot x = sec x csc x
tan x + cot x = (sin x / cos x) + (cos x / )
= (sin² x + cos² x) / (cos x )
= 1 / (cos x sin x)
= (1 / cos x) * (1 / )
= sec x
3. Prove the identity: (1 - cos² θ) / sin θ = sin θ
4. Which of the following is equivalent to (sec² x - 1) / tan x?
sin x
cos x
tan x
cot x
5. The identity sin² θ + cos² θ = 1 is known as the Pythagorean identity.
True
False
6. Prove the identity: (1 + tan² x) / (1 + cot² x) = tan² x