Solve the equation `2(cos x+cos2x)+sin2x(1+2cos x)=2sinx` for `(-pilt=xlt=pi)`

Solve the equation sqrt3cos x + sin x = sqrt2 .

Solve the equation sin^4x+cos^4x-2sin^2x+(3sin^2 2x)/4=0

Solve the equation (sqrt(3))/2sinx-cosx=cos^2x

(cos2x)/(sin ^(2) x cos^(2) x)

prove that [2(sin^3 x - cos^3 x )/(sinx -cosx)]-sin2x=2

Solve sin 2x=4 cos x .

Find the number of solution of the equation 1+e^(cot^2 x )=sqrt(2|sinx|-1)+(1-cos2x)/(1+sin^4x) for x in (0,5pi)dot