Solve `2(cosx+cos2x)+sin2x(1+2cosx)=2sinx,−π≤x≤π`

Solve cosx=(1)/(2) .

Solve 2cos^(2)x+3sinx=0 .

int(sin2x)/((sinx+cosx)^2)dx

Prove that (sinx-sin3x)/(sin^(2)x-cos^(2)x)=2sinx

Integrate the functions (2cosx-3sinx)/(6cosx+4sinx)

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

Prove that : (cosx-cosy)^(2)+(sinx-siny)^(2)=4sin^(2)""(x-y)/(2)

Integrate the function in Exercise. (2cos x-3 sin x)/(6 cosx+4 sin x)

If |[sin2x,cos^2x,cos4x],[cos^2x,cos2x,sin^2x],[cos^4x,sin^2x,sin2x]|=a_0+a_1 (sinx)+a_2(sin^2x)+....+a_n(sin^n x) then the value of a_0 is-