Question

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

• A. less than $1$
• B. Equal to $1$
• C. Greater than or equal to $2$
• D. Greater than 1 but less than $2$
• E. None of the above.

Answer 1

Answer: (C)

Greater than or equal to $2$

We know that,

$A.M\ge G.M$

$\therefore \frac{{\sin }^2\theta +{\csc }^2\theta }{2}\ge \sqrt{{\sin }^2\theta .{\csc }^2\theta }$

or, ${\sin }^2\theta +{\csc }^2\theta \ge 2$ $[\sin \theta .\csc \theta =1]$

Hence, C is the correct option.