如题化简:[(1+sinθ+cosθ)(sinθ/2-cosθ/2)]/√(2+2cosθ)(0<θ<π)

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如题化简:[(1+sinθ+cosθ)(sinθ/2-cosθ/2)]/√(2+2cosθ)(0<θ<π)

(1+sinθ+cosθ)(sinθ/2-cosθ/2)/√(2+2cosθ)
=[2sinθ/2cosθ/2+2(cosθ/2)^2]*(sinθ/2-cosθ/2)/√[4(cosθ/2)^2]
=2cosθ/2*(sinθ/2+cosθ/2)(sinθ/2-cosθ/2)/2绝对值cosθ/2
=cosθ/2*(-cosθ)/绝对值cosθ/2(0<θ<π,0<θ/2<π/2 )
=-cosθ