Question

Prove that ${\sec }^4\theta -{\sec }^2\theta ={\tan }^4\theta +{\tan }^2\theta$

Answer 1

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

$LHS$

${\sec }^4-{\sec }^2\theta$

$\Rightarrow {\sec }^2\theta ({\sec }^2\theta -1)$

$\Rightarrow {\sec }^2\theta \left({\tan }^2\theta \right)$

$\Rightarrow (1+{\tan }^2\theta )\left({\tan }^2\theta \right)$

$\Rightarrow {\tan }^2\theta +{\tan }^4\theta$

$\Rightarrow RHS$

$\Rightarrow LHS=RHS$