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Integration as Antiderivative

52.Prove that...

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52.Prove that cos2xcosx/2-cos3x cos 9x/2= sin 5xsin 5x/2

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\frac{sin 5 x + sin x - 2 sin 3 x}{cos 5 x - cos x} = tan x

cos 2 x cos \frac{x}{2} - cos 3 x cos \frac{9 x}{2} = sin 5 x sin \frac{5 x}{2}

(sin 3 x + sin x) sin x + (cos 3 x - cos x) cos x = 0

cos 38^{o} cos 52^{o} - sin 38^{o} sin 52^{o} = 0

Prove that \frac{cos 7 x + cos 5 x}{sin 7 x - sin 5 x} = cot x

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