Trigonometric Identities|Please help!

Question

please help me understand how to simplify these problems.

a. tan θ + cot θ

⎯⎯⎯⎯⎯⎯⎯

tan θ

b. cos² θ

⎯⎯⎯⎯

1 - sin θ

c. sec² θ - 1

⎯⎯⎯⎯⎯

sec² θ

d. tan θ ccs θ cos θ

Answer 1

a. tan⁡θ/tan⁡θ +cot⁡θ/tan⁡θ = 1+cot^2θ = cosec^2θ

b. We know that cos^2θ+sin^2θ = 1, so cos^2θ = 1-sin^2θ = (1-sinθ) (1+sinθ)

Substitute in the above equation, we get

Cos^2θ = [(1-sinθ) (1+sinθ)]/(1-sinθ) = 1+sinθ

c. (sec^2θ-1)/sec^2θ = 1-cos^2θ = sin^2θ

d. tanθ ccsθ cosθ = (sin θ/cos θ) (1/sinθ) (cosθ) = 1

Answer 2

desmos.com/calculator/zadoct4lws