Question

решить неравенство sin^2 x<1/4

Answer 1

$Sin^{2}x<\dfrac{1}{4}\\\\\dfrac{1-Cos2x}{2}<\dfrac{1}{4} \ | \ \cdot 2\\\\1-Cos2x<\dfrac{1}{2}\\\\-Cos2x<-\dfrac{1}{2} \\\\Cos2x>\dfrac{1}{2}\\\\-\dfrac{\pi }{3}+2\pi n<2x<\dfrac{\pi }{3}+2\pi n,n\in Z\\\\-\dfrac{\pi }{6} +\pi n<x<\dfrac{\pi }{6}+\pi n,n\in Z\\\\\boxed{x\in\Big(-\dfrac{\pi }{6}+\pi n \ ; \ \dfrac{\pi }{6}+\pi n\Big),n\in Z}$