Question

The value of ${\tan }^2\theta {\sec }^2\theta \left({\cot }^2\theta -{\cos }^2\theta \right)$ is

• A. 0
• B. 1
• C. $-1$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

${\tan }^2\theta {\sec }^2\theta \left({\cot }^2\theta -{\cos }^2\theta \right)$
$={\sec }^2\theta \left({\tan }^2\theta {\cot }^2\theta -{\tan }^2\theta {\cos }^2\theta \right)$
$={\sec }^2\theta \left(1-\frac{{\sin }^2\theta }{{\cos }^2\theta }{\cos }^2\theta \right)={\sec }^2\theta .{\cos }^2\theta =1$