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Question Number 136122 by bramlexs22 last updated on 18/Mar/21

$$2(\cos x+\cos 2x)+\sin 2x(1+2\cos x)=2\sin x$$

Answered by EDWIN88 last updated on 18/Mar/21

$$2(2\cos {}^2\mathrm{x}+\cos \mathrm{x}-1)+2\sin \mathrm{xcos}\mathrm{x}(1+2\cos \mathrm{x})-2\sin \mathrm{x}=0$$$$2(2\cos {}^2\mathrm{x}+\cos \mathrm{x}-1)+2\sin \mathrm{x}[2\cos {}^2\mathrm{x}+\cos \mathrm{x}-1]=0$$$$(2\cos {}^2\mathrm{x}+\cos \mathrm{x}-1)+\sin \mathrm{x}(2\cos {}^2\mathrm{x}+\cos \mathrm{x}-1)=0$$$$(1+\sin \mathrm{x})(2\cos \mathrm{x}-1)(\cos \mathrm{x}+1)=0$$$$\{\begin{array}{l}\sin \mathrm{x}=-1\Rightarrow \mathrm{x}=\frac{3\pi }{2}\\ \cos \mathrm{x}=\frac{1}{2}\Rightarrow \mathrm{x}=\frac{\pi }{3};\frac{5\pi }{3}\\ \cos \mathrm{x}=-1\Rightarrow \mathrm{x}=\pi \end{array}$$

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