Question

The value of ${\sec }^2\theta +{\text{cosec}}^2\theta$ is equal to :

• A. ${\tan }^2\theta +{\cot }^2\theta$
• B. ${\sec }^2\theta .{\text{cosec}}^2\theta$
• C. $\sec \theta .\text{cosec}\theta$
• D. ${\sin }^2\theta .{\cos }^2\theta$
• E. 1

Answer 1

Answer: (B)

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

The value of ${\sec }^2\theta +{\text{cosec}}^2\theta$ is

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

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

$=\frac{1}{{\sin }^2\theta {\cos }^2\theta }$ .....[Since ${\sin }^2\theta +{\cos }^2\theta =1$]

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