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Question Number 144822 by mathlove last updated on 29/Jun/21

$$\sin {}^{3}x\cos x-\cos {}^{3}x\sin x=\frac{1}{4}$$$$x=?$$

Answered by ajfour last updated on 29/Jun/21

$$2\sin x\cos x(\sin {}^{2}x-\cos {}^{2}x)=\frac{1}{2}$$$$2\sin 2x\cos 2x=-1$$$$\sin 4x=-1$$$$4x=2n\pi -\frac{\pi }{2}$$$$x=\frac{n\pi }{2}-\frac{\pi }{8}$$

Commented by mathlove last updated on 29/Jun/21

$$thankssir$$

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