cos^2 x - 3sinxcosx + 1 = 0

Question

cos^2 x - 3sinxcosx + 1 = 0

Answer 1

Сos²x-3sinxcosx+1=0
сos²x-3sinxcosx+sin²x+cos²x=0
sin²x-3sinxcosx+2cos²x=0 /cos²x≠0
tg²x-3tgx+2=0
tgx=a
a2-3a+2=0
a1+a2=3 U a1*a2=2
a1=1⇒tgx=1⇒x=π/4+πn
a2=2⇒tgx=2⇒x=arctg2+πn