Question

${\cos }^4\theta +{\cos }^2\theta =1$ then show that ${\sec }^4\theta -{\sec }^2\theta =1$

Answer 1

We have,

${\cos }^4\theta +{\cos }^2\theta =1$

$\frac{1}{{\sec }^4\theta }+\frac{1}{{\sec }^2\theta }=1$

$\frac{1+{\sec }^2\theta }{{\sec }^4\theta }=1$

$1+{\sec }^2\theta ={\sec }^4\theta$

${\sec }^4\theta -{\sec }^2\theta =1$

Hence, proved.