Question

${\sec }^2\theta -\frac{{\sin }^2\theta -2{\sin }^4\theta }{2{\cos }^4\theta -{\cos }^2\theta }=1$.

• A. True
• B. False

Answer 1

The correct option is A True

${\sec }^2\theta -\frac{{\sin }^2\theta -2{\sin }^4\theta }{2{\cos }^4\theta -{\cos }^4\theta }$

$={\sec }^2\theta -\frac{{\sin }^2\theta (1-2{\sin }^2\theta )}{{\cos }^2\theta (2{\cos }^2\theta -1)}$

$={\sec }^2\theta -\frac{{\sin }^2\theta \cos 2\theta }{{\cos }^2\theta \cos 2\theta }$

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

Hence the given statement is true.