根据f（π/4）=1，可排除C、D。F‘(x)=(1+1/f^2(x))f'(x),G(x)=f(x)+1/f(x),F'(x)=G(x)所以(1+1/f^2(x))f'(x)=f(x)+1/f(x)f'(x)=（f(x)+1/f(x))/(1+1/f^2(x))则f(x)=cot(x).所以选B
