The greatest value of `sin^3x + cos^3x` in `[0,pi/2]` is

The greatest value of sin^(3)x+cos^(3)x in [0,(pi)/(2)] is

The greatest value of sin^(3)x+cos^(3)x in [0,(pi)/(2)] is

The greatest value of cos^(2)((pi)/(3)-x)-cos^(2)((pi)/(3)+x) is

Find greatest and least values of f(x)=x-sin2x+1/3sin3x ,\ x\ in [0,\ pi]

If x in [-(5pi)/2,(5pi)/2] , then the greatest positive solution of 1+sin^4x=cos^2 3x is -

The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where [.] denotes the greatest integer function), x in [0, 2pi] , is

The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where [.] denotes the greatest integer function), x in [0, 2pi] , is