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3.Trigonometrical Ratios, Functions and Identities
medium
જો $A + B + C = \pi ,$ તો $\cos \,\,2A + \cos \,\,2B + \cos \,\,2C = $
A
$1 + 4\,\cos A\,\cos B\,\sin C$
B
$ - 1 + 4\,\sin A\,\sin B\,\cos C$
C
$ - 1 - 4\,\cos A\,\,\cos B\,\,\cos C$
D
એકપણ નહિ.
Solution
(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$.
Standard 11
Mathematics
