化简1+sinθ-cosθ/1+sinθ+cosθ详细过程.
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/06/13 13:00:23
化简1+sinθ-cosθ/1+sinθ+cosθ详细过程.
应用公式:
sina=2sina/2*cosa/2
cosa=2(cosa/2)^2-1=1-2(sina/2)^2
(1+sinθ-cosθ0/(1+sinθ+cosθ)
=(1+2sinθ/2*cosθ/2-1+2sin^2θ/2)/(1+2sinθ/2*cosθ/2+2cos^2θ/2-1)
=(2sinθ/2*cosθ/2+2sin^2θ/2)/(2sinθ/2*cosθ/2+2cos^2θ/2)
=2sinθ/2(sinθ/2+cosθ/2)/2cosθ/2(sinθ/2+cosθ/2)
=sinθ/2/cosθ/2
=tanθ/2
sina=2sina/2*cosa/2
cosa=2(cosa/2)^2-1=1-2(sina/2)^2
(1+sinθ-cosθ0/(1+sinθ+cosθ)
=(1+2sinθ/2*cosθ/2-1+2sin^2θ/2)/(1+2sinθ/2*cosθ/2+2cos^2θ/2-1)
=(2sinθ/2*cosθ/2+2sin^2θ/2)/(2sinθ/2*cosθ/2+2cos^2θ/2)
=2sinθ/2(sinθ/2+cosθ/2)/2cosθ/2(sinθ/2+cosθ/2)
=sinθ/2/cosθ/2
=tanθ/2
化简1+sinθ-cosθ/1+sinθ+cosθ详细过程.
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