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Question Number 119506 by bemath last updated on 25/Oct/20

$$\cos \frac{\pi }{5}\cos x+\sin \frac{\pi }{5}\sin x⩽\frac{\sqrt{2}}{2}$$

Answered by 1549442205PVT last updated on 25/Oct/20

$$\cos \frac{\pi }{5}\cos x+\sin \frac{\pi }{5}\sin x⩽\frac{\sqrt{2}}{2}$$$$\iff \cos (\mathrm{x}-\frac{\pi }{5})⩽\cos \frac{\pi }{4}$$$$\iff \mathrm{x}-\frac{\pi }{5}⩾\frac{\pi }{4}+2\mathrm{m}\pi$$$$\iff \frac{\mathit{\pi }}{4}+2\mathbf{m}\mathit{\pi }⩽\mathbf{x}⩽\frac{7\mathit{\pi }}{4}+2\mathbf{m}\mathit{\pi }$$

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