cosx-cos3x-cos5x-cos7x-x-

Question Number 207518 by hardmath last updated on 17/May/24

\cos x \cos 3 x = \cos 5 x \cos 7 x

\Rightarrow x = ?

Answered by Frix last updated on 17/May/24

\cos x \cos 3 x = \cos 5 x \cos 7 x

\frac{\cos 2 x + \cos 4 x}{2} = \frac{\cos 2 x + \cos 12 x}{2}

\cos 4 x = \cos 12 x

\cos y = \cos 3 y

\cos y = (1 - {4 \sin}^{2} y) \cos y

\cos y - (1 - {4 \sin}^{2} y) \cos y = 0

4 \cos y \sin^{2} y = 0

\cos y = 0 \lor \sin y = 0

\cos 4 x = 0 \lor \sin 4 x = 0

x = \frac{(2 n + 1) π}{8} \lor x = \frac{2 n π}{8}

x = \frac{n π}{8}

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