Because f(x)=f'(π/4)cos x+sin x,

So f'(x)=-f'(π/4)sinx+cosx.

So f' (π/4) =-f' (π/4) sin (π/4)+cos (π/4).

That is, f' (π/4) =-√ 2/2f' (π/4)+√ 2/2-①.

f(π/4)=f'(π/4)cos(π/4)+sin(π/4)

So f (π/4) = √ 2/2f' (π/4)+√ 2/2-② formula.

F(π/4)= 1 comes from ① and ②.