Question

${\cos }^2\theta (1+{\tan }^2\theta )+{\sin }^2\theta (1+{\cot }^2\theta )=2$

• A. True
• B. False

Answer 1

The correct option is A True

${\cos }^2\theta (1+{\tan }^2\theta )+{\sin }^2\theta (1+{\cot }^2\theta )={\cos }^2\theta \left({\text{sec}}^2\theta \right)+{\sin }^2\theta \left({\text{cosec}}^2\theta \right)$

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

$=1+1$

$=2$

So the given relation is $\text{True}$