Question

Решить уравнение
5sin^2 5x-2=0

Answer 1

$5sin^25x-2=0;\ sin^2x-frac{2}{5}=0;\ (sin5x-sqrt{frac{2}{5}})(sin5x+sqrt{frac{2}{5}})=0;\ 1) x_1=frac{(-1)^n}{5}cdotarcsin{sqrt{frac{2}{5}}}+frac{pi n}{5},\ 2) x_2=frac{(-1)^n}{5}cdotarcsin(-sqrt{frac{2}{5}})+frac{pi n}{5}=\ =-frac{(-1)^n}{5}cdotarcsin{sqrt{frac{2}{5}}}+frac{pi n}{5};\ x=pmfrac{(-1)^n}{5}cdotarcsin{sqrt{frac{2}{5}}}+frac{pi n}{5}, nin Z$