Question

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

Answer 1

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
$left { {{cosx textless 0} atop {tgx=2}} right.$
$left { {{cosx textless 0} atop {x=arctg2+ pi n}} right.$
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