Question

Prove that
${\sec }^2\theta -\cos e{c}^2\theta ={\tan }^2\theta -{\cot }^2\theta$

Answer 1

${\sec }^2\theta -cose{c}^2\theta$

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

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