Question

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

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

Answer 1

Answer: (A)

3

Answer 2

$\frac { \sin ^ { 2 } A + \sin A + 1 } { \sin A } = \sin A + \frac { 1 } { \sin A } + 1$

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