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Question: If \(A + B + C = \pi,\) then \(\frac{\cos A}{\sin B\sin C} + \frac{\cos B}{\sin C\sin A} + \frac{\co...

If A+B+C=π,A + B + C = \pi, then cos⁡Asin⁡Bsin⁡C+cos⁡Bsin⁡Csin⁡A+cos⁡Csin⁡Asin⁡B=\frac{\cos A}{\sin B\sin C} + \frac{\cos B}{\sin C\sin A} + \frac{\cos C}{\sin A\sin B} =

A

0

B

1

C

2

D

3

Answer

2

Explanation

Solution

L.H.S. =12sin⁡2A+sin⁡2B+sin⁡2Csin⁡Asin⁡Bsin⁡C=2= \frac{1}{2}\frac{\sin 2A + \sin 2B + \sin 2C}{\sin A\sin B\sin C} = 2.