作业帮三角恒等变换,化简:(1+sinθ+cosθ)(sinθ/2-cosθ/2)/√2+2cosθ
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三角恒等变换,化简:(1+sinθ+cosθ)(sinθ/2-cosθ/2)/√2+2cosθ
三角恒等变换,化简:(1+sinθ+cosθ)(sinθ/2-cosθ/2)/√2+2cosθ
三角恒等变换,化简:(1+sinθ+cosθ)(sinθ/2-cosθ/2)/√2+2cosθ
1+sinθ+cosθ=2(cosθ/2)^2+2sin(θ/2)cos(θ/2)=2cos(θ/2)[cos(θ/2)+sin(θ/2)]
∴分子=2cos(θ/2){[sin(θ/2)]^2-[cos(θ/2)]^2}=-2cos(θ/2)*cosθ
分母=√{2*2[cos(θ/2)]^2}=2|cos(θ/2)|
∴原式=-2cos(θ/2)*cosθ/{2|cos(θ/2)|}=-cos(θ/2)*cosθ/|cos(θ/2)|=±cosθ