Aspire Faculty ID #13936 · Topic: JAMIA MILLIA ISLAMIA MCA 2020 · Just now
JAMIA MILLIA ISLAMIA MCA 2020

What will be the value of $f(x) = (\sin 3x + \sin x)\sin x + (\cos 3x - \cos x)\cos x$ ?

Solution

$f(x) = (\sin 3x + \sin x)\sin x + (\cos 3x - \cos x)\cos x$ $= \sin 3x \sin x + \sin^2 x + \cos 3x \cos x - \cos^2 x$ Using identity $\cos A \cos B + \sin A \sin B = \cos(A - B)$: $f(x) = \cos(3x - x) + (\sin^2 x - \cos^2 x)$ $= \cos 2x - \cos 2x = 0$

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