I'm trying to symbolic minimize a function composed of sine and cosine. As the target function has local minima at the outside of the input domain, setting derivative of the target function as zero can not be used. So I want to use the Minimize, but it seems that it doesn't work for trigonometric function. Simplist version of target function is expressed as follows:
f[x_]:=M*Cos[x]^2;
Minimize[{f[x],0<=x<=pi/2, M>0}, x]
And I can get the output as follows:
Out[]=Minimize[{M Cos[x]^2, 0 <= x <= \[Pi]/2 && M > 0}, x]
I think Minimize doesn't work properly for trigonometric functions. Is there any way to symbolic minimize the trigonometric function?