Question

Find the minimum value of ${\csc }^2\theta +{\sin }^2\theta$

• A. 0
• B. $-1$
• C. 1
• D. 2

Answer 1

The correct option is D 2

${\csc }^2\theta +{\sin }^2\theta =\frac{1}{{\sin }^2\theta }+{\sin }^2\theta ={(\frac{1}{\sin \theta }-\sin \theta )}^2+2$

$\therefore$ Minimum value of ${\csc }^2\theta +{\sin }^2\theta =2$

[because the minimum value of $(\frac{1}{\sin \theta }-\sin \theta )$ is 0]