f(x)=(cosx)²+sinx那么f(x-π/2)=cos²(x-π/2)+sin(x-π/2)=sin²x-cosx=1-cos²x-cosx=5/4-(cosx+1/2)²因为x∈[0,π/2]所以cosx∈[0,1]故f(x)的最大值是5/4-(0+1/2)²=1
