Question

The value of ${\text{cosec}}^2({90}^o-\theta )-{\tan }^2\theta$ is :

• A. $2$
• B. $3$
• C. $0$
• D. $1$

Answer 1

The correct option is D $1$

The value of ${\text{cosec}}^2(90-\theta )-{\tan }^2\theta$ is

$={\sec }^2\theta -{\tan }^2\theta$

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

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

$=1$