Question

Solve:

${\sin }^4\theta +2{\cos }^2\theta (1-\frac{1}{{\sec }^2\theta })+{\cos }^4\theta$

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

Answer 1

The correct option is A $1$

${\sin }^4\theta +2{\cos }^2\theta (1-\frac{1}{{\sec }^2\theta })+{\cos }^4\theta$

$={\sin }^4\theta +2{\cos }^2\theta (1-{\cos }^2\theta )+{\cos }^4\theta$

$={\sin }^4\theta +2{\cos }^2\theta .{\sin }^2\theta +{\cos }^4\theta$

$={({\sin }^2\theta +{\cos }^2\theta )}^2$

$=1^2=1$