5sin² x + 2sinx cosx - cos² x = sin² x + cos² x
5sin² x - sin² x + 2sinx cosx - cos²x - cos² x =0
4sin² x + 2sinx cosx - 2cos² x =0
2sin² x + sinx cosx - cos² x =0
2sin² x + sinx cosx - cos² x = 0
cos² x cosx cosx cos²x cos² x
2tg² x + tgx - 1 =0
Замена у=tgx
2y² +y -1 =0
D=1+8=9
y₁ = -1 -3 = -1
4
y₂ = -1+3 =2/4 = 1/2
4
При у= -1
tgx = -1
x= -π/4 + πk, k∈Z
При у=1/2
tgx= 1/2
x=arctg1/2 + πk, k∈Z
Ответ: -π/4 + πk, k∈Z;
arctg1/2 + πk, k∈Z.