Question

Prove:
${\cot }^2\theta -ta{n}^2\theta ={\csc }^2\theta -{\sec }^2\theta$

Answer 1

To prove,

${\cot }^2\theta -{\tan }^2\theta ={\csc }^2\theta -{\sec }^2\theta$

Let's take,

${\cot }^2\theta +{\sec }^2\theta =({\csc }^2\theta -1)+(1+{\tan }^2\theta )$

${\cot }^2\theta +{\sec }^2\theta ={\csc }^2\theta +{\tan }^2\theta$

$\Rightarrow {\cot }^2\theta -{\tan }^2\theta ={\csc }^2\theta -{\sec }^2\theta$