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Question Number 112173 by bobhans last updated on 06/Sep/20

$$\mathrm{find}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{equation}$$$$\sqrt{\cos 2\mathrm{x}-\sin {}^3\mathrm{x}+3}=\sin \mathrm{x}$$

Answered by john santu last updated on 06/Sep/20

$$since\sin x⩾0,then$$$$\cos 2x-\sin {}^{3}x+3=\sin {}^{2}x$$$$1-2\sin {}^{2}x-\sin {}^{3}x+3=\sin {}^{2}x$$$$\sin {}^{3}x+3\sin {}^{2}x-4=0$$$$(\sin x-1)(\sin {}^2+4\sin x+4)=0$$$$(\sin x-1){(\sin x+2)}^2=0$$$$\sin x=1\to x=\frac{\pi }{2}+k.2\pi ;k\in \mathbb{Z}$$

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