If A + B + C = pi , then cos , 2A + cos , 2B | vedclass

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(C) Given $A + B + C = \pi$,so $A + B = \pi - C$. $L.H.S. = \cos 2A + \cos 2B + \cos 2C$ $= 2 \cos (A + B) \cos (A - B) + (2 \cos^2 C - 1)$ $= 2 \cos

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

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(C) Given $A + B + C = \pi$,so $A + B = \pi - C$. $L.H.S. = \cos 2A + \cos 2B + \cos 2C$ $= 2 \cos (A + B) \cos (A - B) + (2 \cos^2 C - 1)$ $= 2 \cos (\pi - C) \cos (A - B) + 2 \cos^2 C - 1$ $= - 2 \cos C \cos (A - B) + 2 \cos^2 C - 1$ $= - 1 - 2 \cos C [\cos (A - B) - \cos C]$ Since $C = \pi - (A + B)$,$\cos C = - \cos (A + B)$. $= - 1 - 2 \cos C [\cos (A - B) + \cos (A + B)]$ $= - 1 - 2 \cos C [2 \cos A \cos B]$ $= - 1 - 4 \cos A \cos B \cos C$.

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

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