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f'(x)=-f'(π/4)sinx+cosx
f'(π/4)=-f'(π/4)sin(π/4)+cos(π/4)
=√2/2-(√2/2)f'(π/4)
f'(π/4)=(√2/2)/(1+√2/2)
=√2/(2+√2)
则
f(π/4)=f'(π/4)cos(π/4)+sin(π/4)
=[√2/(2+√2)]×(√2/2)+√2/2
=1/(2+√2)+√2/2
f'(π/4)=-f'(π/4)sin(π/4)+cos(π/4)
=√2/2-(√2/2)f'(π/4)
f'(π/4)=(√2/2)/(1+√2/2)
=√2/(2+√2)
则
f(π/4)=f'(π/4)cos(π/4)+sin(π/4)
=[√2/(2+√2)]×(√2/2)+√2/2
=1/(2+√2)+√2/2
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