## Does fn(x)=cosn(x)(1−cosn(x))f_n(x)=\cos^n(x)(1-\cos^n(x)) converge uniformly for xx in [π/4 , π/2][π/4 , π/2]?

Does f_n(x)=\cos^n(x)(1-\cos^n(x)) converge uniformly for x in [π/4 , π/2]? Its clear to see that the point-wise convergence is to 0. By finding the derivative I obtained that the maximum of f_n is when \cos^n(x)=1/2 and that \sup |f_n(x)-0|= 1/2\cdot(1-1/2)=1/4 which would indicate that the function does not converge uniformly, however I’m not sure the … Read more