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Question Number 147810 by mathdanisur last updated on 23/Jul/21

$$\mathit{c}\mathit{o}\mathit{s}\left(\mathit{x}\right)\cdot \mathit{c}\mathit{o}\mathit{s}\left(3\mathit{x}\right)=\mathit{c}\mathit{o}\mathit{s}\left(5\mathit{x}\right)\cdot \mathit{c}\mathit{o}\mathit{s}\left(7\mathit{x}\right)$$$$\mathit{x}=?$$

Answered by gsk2684 last updated on 23/Jul/21

$$2\cos x\cos 3x=2\cos 5x\cos 7x$$$$\cos (3x+x)+\cos (3x-x)=\cos (7x+5x)+\cos (7x-5x)$$$$\cos 4x=\cos 12x$$$$12x=2n\pi \pm 4x,n\in Z$$$$16x=2n\pi or8x=2n\pi$$$$x=\frac{n\pi }{8}or\frac{n\pi }{4}$$

Commented by mathdanisur last updated on 23/Jul/21

$$ThankyouSir$$

Commented by peter frank last updated on 24/Jul/21

$$thankyou$$

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