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Question: If A + B + C = p and \(\sum_{}^{}{\cos A}\)cosec B cosec C = k, then k =...

If A + B + C = p and ∑cos⁡A\sum_{}^{}{\cos A}cosec B cosec C = k, then k =

A

2\sqrt{2}

B

3

C

2

D

3\sqrt{3}

Answer

2

Explanation

Solution

Sol. ∑cos⁡A\sum_{}^{}{\cos A}cosec B cosec C = k

Ž ∑∑sin⁡\sum_{}^{\sum}\sinA cos A = k sin B sin C sin A

∑∑sin⁡\sum_{}^{\sum}\sin2A = 2k sin A sin B sin C

Now in a D, ∑∑sin⁡\sum_{}^{\sum}\sin2A = 4 sin A sin B sin C

\ k = 2