Question

State true or false.

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

• A. True
• B. False

Answer 1

The correct option is A True

${\text{sec}}^4\theta -{\tan }^4\theta =({\text{sec}}^2\theta {)}^2-({\tan }^2\theta {)}^2$

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

$={\text{sec}}^2\theta +{\tan }^2\theta$

$=1+{\tan }^2\theta +{\tan }^2\theta$

$=1+2{\tan }^2\theta$

So the relation is $\text{True}$