Question

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

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

Answer 1

Answer: (D)

${\sec }^2\theta .{\text{cosec}}^2\theta$

${\sec }^2\theta +{\text{cosec}}^2\theta =\frac{1}{{\cos }^2\theta }+\frac{1}{{\sin }^2\theta }=\frac{{\sin }^2\theta +{\cos }^2\theta }{{\sin }^2\theta .{\cos }^2\theta }=\frac{1}{{\sin }^2\theta .{\cos }^2\theta }={\text{cosec}}^2\theta .{\sec }^2\theta$