Question

PLEASE HELP

Prove that (tanθ + cotθ)² = sec²θ + cosec²θ

I've tried using identities but can't figure it out.

Answer 1

whats tan0?

Answer 2

\[(\tan\theta + \cot\theta)^2 = \tan^2 \theta + \cot^2\theta + 2\tan\theta \cot\theta\]\[= \color{#c00}{\tan^2\theta} + \color{blue}{\cot^2\theta} + 2\]\[= \color{#c00}{\sec^2\theta - 1}+\color{blue}{\csc^2\theta - 1} + 2\]\[= \sec^2 \theta + \csc^2\theta\]