Question

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

Answer 1

Given that,

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

Divided by ${\cos }^4\theta$ on both sides ,we gate

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

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

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

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

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

Hence option $\left(1\right)$ is correct ans