Solve `sin2x-cos2x=sinx-cosx`

The maximum value of 4sin^2x+3cos^2x+sinx/2+cosx/2 is

Solve 4sinx.sin2x.sin4x=sin3x

If f(x)=|{:(2cos^(2)x,sin2x,-sinx),(sin2x,2sin^(2)x,cosx),(sinx,-cosx,0):}|" then "int_(0)^(pi//2)[f(x)+f'(x)]dx=

The number of values of y in [-2pi,2pi] satisfying the equation |sin2x|+|cos2x|=|siny| is