Cos^2x + 4sinxcosx = 2

Cos^2x + 4sinxcosx = 2

сos^2 x + 4sinxcosx = 2 (cos^2 x+sin^2 x)

сos^2 x + 4sinxcosx - 2cos^2 x-2sin^2 x=0

-cos^2x + 4sinxcosx - 2sin^2 x=0

cos^2x - 4sinxcosx + 2sin^2 x=0

(cosx+2sinx) ^2=0

cosx+2sinx=0 (делим обе части на cos x не равный 0)

1+2tgx=0

2tgx=-1

tgx=-1/2

x=-arctg1/2 + Пn