Question

${\tan }^4\theta +{\tan }^2\theta$ is equal to

• A. ${\sec }^2-{\sec }^4\theta$
• B. ${\sec }^4\theta -{\sec }^2\theta$
• C. ${\sin }^4\theta -{\sec }^2\theta$
• D. ${\sin }^4\theta -{\cos }^2\theta$

Answer 1

The correct option is B ${\sec }^4\theta -{\sec }^2\theta$

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