Question

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Решите неравенство: sin^2 x<=0,25

Answer 1

$sin^2x\leq 0,25\\\\\frac{1-cos2x}{2}\leq \frac{1}{4}\\\\1-cos2x\leq \frac{1}{2}\\\\cos2x\geq \frac{1}{2}\\\\-\frac{\pi }{3}+2\pi n\leq 2x\leq \frac{\pi }{3}+2\pi n\; ,\; n\in Z\\\\-\frac{\pi }{6}+\pi n \leq x\leq \frac{\pi }{6}+\pi n\; ,\; n\in Z$