Question

In any triangle ABC, Π$\left[ \frac { \sin ^ { 2 } \mathrm {~A} + \sin \mathrm { A } + 1 } { \sin \mathrm {~A} } \right]$ is always greater than

• A. 9
• B. 3
• C. 27
• D. 10

Answer 1

Answer: (C)

27

Answer 2

By AM ≥ GM

sin A + + 1 > 2 + 1 = 3

Now π $\left( \sin \mathrm { A } + \frac { 1 } { \sin \mathrm {~A} } + 1 \right)$> 3.3.3 = 27