જો A, B, C ત્રિકોણના ખૂણા હોય તો sin 2A + sin | vedclass

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Question

(d) $\sin 2A + \sin 2B\, - \sin 2C$

$= 2\sin A\cos A + 2\cos (B + C)\sin (B - C)$

$\{ \because A + B + C = \pi ,\,	herefore \,B + C = \pi

Vedclass · Accepted Answer

$4\cos A\,\cos B\,\sin C$

Vedclass · Answer

(d) $\sin 2A + \sin 2B\, - \sin 2C$

$= 2\sin A\cos A + 2\cos (B + C)\sin (B - C)$

$\{ \because A + B + C = \pi ,\,	herefore \,B + C = \pi  - A,\cos (B + C) = \cos (\pi  - A),$ $\cos (B + C) = - \cos A,\,\sin (B + C) = \sin A\} $

$ = 2\cos A\,\,[\sin A - \sin (B - C)]$

$ = 2\cos A\,[\sin (B + C) - \sin (B - C)]$

$ = 2\cos A.2\cos B.\sin C$$ = 4\cos A.\,\cos B.\,\sin C$.

Trick : First put $A = B = C = {60^o}$ for, these values.

Options $(a)$ and $ (d)$ satisfies the condition, Now put $A = B = 45^\circ $ and $c = {90^o}$.

Then only $(d)$ satisfies. Hence $(d)$ is the answer.

જો $A, B, C$ ત્રિકોણના ખૂણા હોય તો $\sin 2A + \sin 2B - \sin 2C$ મેળવો.

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