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Prove that cos3x = 4cos3x - 3cosx. |
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Answer» Take cos(A+B) =cos Acos B - sin Asin B Put A = x, B = 2x ∴ cos(x + 2x) = cos x.cos2x - sin x sin 2x cos(3x) = cos x(2cos2x - 1) - sin x(2 sin cos x) = 2cos3x - cosx - 2cosx(sin2x) = 2cos3x - cosx - 2cosx(1 - cos2x). = 2 cos3x - cosx - 2 cosx + 2cos3x [4cos3r - 3cosx.] |
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