Question

Prove the following trigonometric identities:

Answer 1

Convert everything to terms of sine and cosine:

$\dfrac{\sec\theta}{\tan\theta}=\dfrac{\frac1{\cos\theta}}{\frac{\sin\theta}{\cos\theta}}$

The factors of $\dfrac1{\cos\theta}$ cancel to give

$\dfrac1{\sin\theta}=\csc\theta$