Question

Prove :

$2{\sec }^2\theta -{\sec }^4\theta -2cose{c}^2\theta +cose{c}^4\theta ={\cot }^4\theta -{\tan }^4\theta$

Answer 1

LHS :

$2{\sec }^2\theta -{\sec }^4\theta -2cose{c}^2\theta +cose{c}^4\theta$

$=(cose{c}^4\theta -2cose{c}^2\theta )-({\sec }^4\theta -2{\sec }^2\theta )$

$=(cose{c}^4\theta -2cose{c}^2\theta +1)-({\sec }^4\theta -2{\sec }^2\theta +1)$

$=(cose{c}^2\theta -1{)}^2-({\sec }^2\theta -1{)}^2$

$={\cot }^4\theta -{\tan }^4\theta$

= RHS