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Question Number 92461 by jagoll last updated on 07/May/20

$$\cos (\frac{3\mathrm{x}}{4}-\pi )=\sin (\frac{\pi }{4}-2\mathrm{x})$$$$\mathrm{x}\in [0,\pi ]$$

Commented by john santu last updated on 07/May/20

$$-\cos \left(\frac{3\mathrm{x}}{4}\right)=\sin (\frac{\pi }{4}-2\mathrm{x})$$$$\cos \left(\frac{3\mathrm{x}}{4}\right)=\sin (2\mathrm{x}-\frac{\pi }{4})$$$$\cos \left(\frac{3\mathrm{x}}{4}\right)=\cos (\frac{\pi }{2}+\frac{\pi }{4}-2\mathrm{x})$$$$\{\begin{array}{l}\frac{11\mathrm{x}}{4}=\frac{3\pi }{4}+2\mathrm{k}\pi \\ -\frac{5\mathrm{x}}{4}=-\frac{3\pi }{4}+2\mathrm{k}\pi \end{array}$$$$\{\begin{array}{l}\mathrm{x}=\frac{3\pi }{11}+\frac{8\mathrm{k}\pi }{11}\\ \mathrm{x}=\frac{3\pi }{5}-\frac{8\mathrm{k}\pi }{5}\end{array}$$

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