Sin^2 x - 3 sin x *cos x + 2 cos^2 = 0

Question

Sin^2 x - 3 sin x *cos x + 2 cos^2 = 0

Answer 1

Sin²x-3sinx*cosx+2cos²x=0 |:cos²x≠0
tg²x-3tgx+2=0
Замена: a=tgx
a²-3a+2=0
a(1)=1, a(2)=2
tgx=1                           tgx=2
x=π/4+πn, n∈Z         x=arctg2+πn, n∈Z