trigonometry inequation

Question

solve for x: cos(2x)+2*sinx*cosx>0

Answer 1

I went to desmos and graphed the function y = cos(2x)+2*sin(x)*cos(x)

It is positive on the interval (-pi/8, 3*pi/8);

the width of this interval is always pi/2;

It happens every pi/2, so the next interval is (7*pi/8, 11*pi/8)

Then again (15*pi/8, 19*pi/8)

It also goes backwards from (-pi/8, 3*pi/8) , so

(-9*pi/8, -5*pi/8)

(-17*pi/8, -13*pi/8)

etc