M=sin^6x -cos ^6x =( sin^2x - cos^2 x )^3 +3 (sin^4x cos^2x-sin^2xcos^4x)=(-cos2x)^3 +3sin^2x.cos^2x.(-cos2x) =(-cos2x)^3+3. (Sin2x)^2/4.(-cos2x) = (-cos2x)^3+3/4.(1 - cos^2(2x)).(-cos2x)= -1/4.cos^3(2x) -3/4. cos2x M max =1 khi cos2x =-1 <-> 2x = pi + k2pi <-> x= pi/2 + k.pi