Question

If A + B + C= pi, Cos A= cos B. cos c, show that 2cot B 2cot c=1

Answer 1

A + B + C = 180 degrees
implies A = 180 – ( B + C )
cos A = cos B cos C
implies cos (180 – B – C) = cos B cos C
implies – cos ( B + C ) = cos B cos C
implies – cos B cos C + sin B sin C = cos B cos C
implies 2 cos B cos C = sin B sin C
Hence cot B cot C = ½
so 2 cot B cot C =1

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