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Question
सिद्ध कीजिए: (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0
Sum
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Solution
बायाँ पक्ष = (sin 3x + sin x) sin x + (cos 3x – cos x) cosx
= sin 3x sin x + sin2x + cos 3x cos x – cos2x
= (cos 3x cos x + sin 3x sin x) – (cos2 x – sin2x)
= cos (3x - x) - cos 2x
= cos 2x – cos 2x
= 0 [∵ cos (A – B) = cos A cos B + sin A sin B]
= दायाँ पक्ष।
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