Question

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

Answer 1

$L.H.S.$

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

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

$({\sec }^2\theta -1)\left({\sec }^2\theta \right)$ $\because {\tan }^2\theta +1={\sec }^2\theta$

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