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Question Number 208686 by hardmath last updated on 21/Jun/24

$${\cos }^{2}2\mathrm{x}={\sin }^{2}2\mathrm{x}+\frac{\sqrt{3}}{2}$$$$\mathrm{x}=?$$

Answered by MM42 last updated on 21/Jun/24

$${cos}^{2}2x-{sin}^{2}2x=\frac{\sqrt{3}}{2}$$$$cos4x=\frac{\sqrt{3}}{2}\Rightarrow 4x=2k\pi \pm \frac{\pi }{6}$$$$\Rightarrow x=\frac{k\pi }{2}\pm \frac{\pi }{24}✓$$$$$$

Commented by hardmath last updated on 28/Jun/24

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{professor}$$

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