Question

If $\frac{\cos A}{\sin B\sin C} + \frac{\cos B}{\sin C\sin A} + \frac{\cos C}{\sin A\sin B} =$then $32\sin\left( \frac{A}{2} \right)\sin\left( \frac{5A}{2} \right) =$

• A. 7
• B. 8
• C. 11
• D. None of these

Answer 1

Answer: (C)

11

Answer 2

$32\sin\frac{A}{2}\sin\frac{5A}{2} = 16(\cos 2A - \cos 3A)$

$= 16(2\cos^{2}A - 1 - 4\cos^{3}A + 3\cos A)$

$= 16\left( 2 \times \frac{9}{16} - 1 - 4 \times \frac{27}{64} + 3 \times \frac{3}{4} \right) = 11$.