2 sinx + | cosx | - 3 cos x=0 решите уравнение

2sinx + |cosx| - 3 cos x=0
Если cosx<0<br>2sinx - cosx- 3 cos x=0
2sinx - 4cosx=0
sinx - 2cosx=0 | ÷cosx≠0
tgx-2=0
tgx=2
$\left \{ {{cosx\ \textless \ 0} \atop {tgx=2}} \right.$
$\left \{ {{cosx\ \textless \ 0} \atop {x=arctg2+ \pi n}} \right.$
x=π+arctg2+2πn, n∈z

Если cosx≥0
2sinx +cosx- 3 cos x=0
2sinx - 2cosx=0
sinx - cosx=0
√2sin(x-π/4)=0
$\left \{ {{cosx \geq 0} \atop {x- \pi /4= \pi k}} \right.$
$\left \{ {{cosx \geq 0} \atop {x=\pi /4+ \pi k}} \right.$
x=π/4+2πk, k∈z
Ответ. x=π+arctg2+2πn, n∈z
x=π/4+2πk, k∈z