Question

${\sec }^{2}6+{\text{cosec}}^{2}6$ is equal to:

• A. ${\sec }^{2}6.{\cot }^{2}6$
• B. ${\sec }^{2}6.{\tan }^{2}6$
• C. ${\text{cosec}}^{2}6.{\cot }^{2}6$
• D. ${\text{cosec}}^{2}6.{\sec }^{2}6$

Answer 1

The correct option is D ${\text{cosec}}^{2}6.{\sec }^{2}6$

${\sec }^{2}6+{\text{cosec}}^{2}6$

$=\frac{1}{{\cos }^{2}6}+\frac{1}{{\sin }^{2}6}$

$=\frac{{\sin }^{2}6+{\cos }^{2}6}{{\sin }^{2}6{\cos }^{2}6}$

$={\sec }^{2}6{\text{cosec}}^{2}6$