3cos^2x-sin^2+2sinx*cosx=0

3cos^2 (x) - sin^2 (x) + 2sinx · cosx =

= 3cos^2 (x) + 3sinx · cosx - sin^2 (x) - sinx · cosx =

= 3cosx (sinx + cosx) - sinx (sinx + cosx) =

= (sinx + cosx) (3cosx - sinx) = 0;

1) sinx + cosx = 0;

Разделим на cosx;

tgx = - 1;

x = - п/4 + пn (n ∈ Z);

2) (3cosx - sinx) = 0;

3cosx = sinx;

Разделим на cosx;

tgx = 3;

x = пk + arctg (3) (k ∈ Z).

Ответ: x = - п/4 + пn (n ∈ Z) или x = пk + arctg (3) (k ∈ Z).