f(x)=2cosx/2×(√2sin(x/2+π/4）+ tan(x/2+π/4)×tan(x/2－π/4))
=2cos(x/2)*√2*[sin(x/2)cos(π/4)+cos(x/2)sin(π/4)] -tan(π/4+x)tan(π/4-x)
=2cos(x/2)[sin(x/2)+cos(x/2)]-tan(π/4+x)*cot(π/4+x)
=2cos(x/2)sin(x/2)+2cos²(x/2)-1
=sinx+cosx
=√2sin(x+π/4)
f(x)=2cosx/2×(√2sin(x/2+π/4）+ tan(x/2+π/4)×tan(x/2－π/4))
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