Question

The value of $({\sin }^2\theta +{\text{cosec}}^2\theta )$ is always

• A. Less than $1$
• B. Equal to $1$
• C. Greater than or equal to $2$
• D. Greater than $1$ but less than $2$

Answer 1

The correct option is C Greater than or equal to $2$

$({\sin }^2\theta +{\text{cosec}}^2\theta )={\sin }^2\theta +\frac{1}{{\sin }^2\theta }$

$=\left[\frac{{\sin }^4\theta +1}{{\sin }^2\theta }\right]$

$\therefore$ $\sin \theta$ is always lies between $0$ $\xi$ $1$ for all possible values of $0.$

$\therefore$ Value of $({\sin }^2\theta +{\text{cosec}}^2\theta )$ greater than equal to $2.$

Hence, the answer is greater than equal to 2.