Question

|sin(x)|=cos(x)
Решить уравнение

Answer 1

$|sin x|=cos x$

Раскроем модуль:

$left[begin{array}{l} left{begin{array}{l} sin x=cos x \ sin xgeq 0 end{array}\ left{begin{array}{l} -sin x=cos x \ sin x<0 end{array}end{array}$

$left[begin{array}{l} left{begin{array}{l} mathrm{tg} x=1 \ sin xgeq 0 end{array}\ left{begin{array}{l} mathrm{tg} x=-1 \ sin x<0 end{array}end{array}$

$left[begin{array}{l} left{begin{array}{l} x=frac{pi }{4}+pi k \ sin xgeq 0 end{array}\ left{begin{array}{l} x=-frac{pi }{4}+pi k \ sin x<0 end{array}end{array}$

$left[begin{array}{l} x=frac{pi }{4}+2pi k \ x=-frac{pi }{4}+2pi k end{array}$

$x=pmdfrac{pi }{4}+2pi k, kinmathbb{Z}$

Ответ: $pmdfrac{pi }{4}+2pi k, kinmathbb{Z}$