If A + B + C = , then , ,2A + , ,2B + , ,2C = - Vidyadip

MCQ

If $A + B + C = \pi ,$ then $\cos \,\,2A + \cos \,\,2B + \cos \,\,2C = $

A
$1 + 4\,\cos A\,\cos B\,\sin C$
B
$ - 1 + 4\,\sin A\,\sin B\,\cos C$
✓
$ - 1 - 4\,\cos A\,\,\cos B\,\,\cos C$
D
None of these

✓

Answer

Correct option: C.

$ - 1 - 4\,\cos A\,\,\cos B\,\,\cos C$

c
(c) $L.H.S.$ $ = 2\cos (A + B)\cos (A - B) + (2{\cos ^2}C - 1)$

$ = - 1 - 2\cos C\cos (A - B) + 2{\cos ^2}C$

$ = - 1 - 2\cos C[\cos (A - B) + \cos (A + B)]$

$ = - 1 - 4\cos A\cos B\cos C$.

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