Question

Решить уравнение 5sin^2 5x-2=0

Answer 1

$5\sin^25x-2=0;\\ \sin^2x-\frac{2}{5}=0;\\ (\sin5x-\sqrt{\frac{2}{5}})(\sin5x+\sqrt{\frac{2}{5}})=0;\\ 1) x_1=\frac{(-1)^n}{5}\cdot\arcsin{\sqrt{\frac{2}{5}}}+\frac{\pi n}{5},\\ 2) x_2=\frac{(-1)^n}{5}\cdot\arcsin(-\sqrt{\frac{2}{5}})+\frac{\pi n}{5}=\\ =-\frac{(-1)^n}{5}\cdot\arcsin{\sqrt{\frac{2}{5}}}+\frac{\pi n}{5};\\ x=\pm\frac{(-1)^n}{5}\cdot\arcsin{\sqrt{\frac{2}{5}}}+\frac{\pi n}{5}, n\in Z$