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

2sinx + |cosx| - 3 cos x=0 Если cosx<0 2sinx - cosx- 3 cos x=0 2sinx - 4cosx=0 sinx - 2cosx=0 | ÷cosx≠0 tgx-2=0 tgx=2 [latex] \left \{ {{cosx\ \textless \ 0} \atop {tgx=2}} \right. [/latex] [latex] \left \{ {{cosx\ \textless \ 0} \atop {x=arctg2+ \pi n}} \right. [/latex] 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 [latex] \left \{ {{cosx \geq 0} \atop {x- \pi /4= \pi k}} \right. [/latex] [latex] \left \{ {{cosx \geq 0} \atop {x=\pi /4+ \pi k}} \right. [/latex] x=π/4+2πk, k∈z Ответ. x=π+arctg2+2πn, n∈z             x=π/4+2πk, k∈z