Question

The value of ${\sin }^{2}q.{\cos }^{2}q({\sec }^{2}q+\text{c}ose{c}^{2}q)$ is

• A. $2$
• B. $4$
• C. $1$
• D. $0$

Answer 1

The correct option is C $1$

Given: ${\sin }^{2}q{\cos }^{2}q({\sec }^{2}q+{\text{cosec}}^{2}q)$
$={\sin }^{2}q{\cos }^{2}q(\frac{1}{{\cos }^{2}q}+\frac{1}{{\sin }^{2}q})$

$={\sin }^{2}q{\cos }^{2}q\left(\frac{{\sin }^{2}q+{\cos }^{2}q}{{\sin }^{2}q{\cos }^{2}q}\right)$

$={\sin }^{2}q+{\cos }^{2}q=1$