Question

In any $\Delta ABC$, the least value of $\left(\frac{{\sin }^{2}A+\sin A+1}{\sin A}\right)$ is

• A. None of these
• B. $\sqrt{3}$
• C. 9
• D. 3

Answer 1

The correct option is D 3

$\frac{{\sin }^{2}A+\sin A+1}{\sin A}=\sin A+\frac{1}{\sin A}+1$
$=[{(\sqrt{\sin A}-\frac{1}{\sqrt{\sin A}})}^2+3]⩾3$

Hence the correct answer is Option A.