存在,f(x)连续可导
故要使f(x)为常数,则f'(x)=0恒成立
而f'(x)=k(sinx)^(k-1)sin(k-1)x-k(cosx)^(k-1)sin(k-1)x+2k(cos2x)^(k-1)sin2x
=k(sinx)^(k-1)sin(k-1)x-k(cosx)^(k-1)sin(k-1)x+k(cos2x)^(k-2)sin4x
可以检验当k=3时,f'(x)=0,此时必有f(x)为常数.