Trigonometric Identity Proofs Worksheet

Trigonometric Identity Proofs

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?

5. The identity sin² θ + cos² θ = 1 is known as the Pythagorean identity.

6. Prove the identity: (1 + tan² x) / (1 + cot² x) = tan² x