化简:根号下 (1-cosθ)/(1+cosθ) + 根号下(1+cosθ)/(1-cosθ)
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/06/25 03:10:46
化简:根号下 (1-cosθ)/(1+cosθ) + 根号下(1+cosθ)/(1-cosθ)
![化简:根号下 (1-cosθ)/(1+cosθ) + 根号下(1+cosθ)/(1-cosθ)](/uploads/image/z/4381423-7-3.jpg?t=%E5%8C%96%E7%AE%80%EF%BC%9A%E6%A0%B9%E5%8F%B7%E4%B8%8B+%281-cos%CE%B8%29%2F%281%2Bcos%CE%B8%29+%2B+%E6%A0%B9%E5%8F%B7%E4%B8%8B%281%2Bcos%CE%B8%29%2F%281-cos%CE%B8%29)
√[(1-cosθ)/(1+cosθ) ]+ [(1+cosθ)/(1-cosθ)]
=√[(1-cosθ)^2/(1+cosθ)(1-cosθ) ]+ [(1+cosθ)^2/(1+cosθ)(1-cosθ)]
=√(1-cosθ)^2/(sinθ)^2 ]+ √(1+cosθ)^2/(sinθ)^2]
=(1-cosθ)/∣sinθ∣+ (1+cosθ)/∣sinθ∣
=(1-cosθ +1+cosθ)/∣sinθ∣
=2/∣sinθ∣
=√[(1-cosθ)^2/(1+cosθ)(1-cosθ) ]+ [(1+cosθ)^2/(1+cosθ)(1-cosθ)]
=√(1-cosθ)^2/(sinθ)^2 ]+ √(1+cosθ)^2/(sinθ)^2]
=(1-cosθ)/∣sinθ∣+ (1+cosθ)/∣sinθ∣
=(1-cosθ +1+cosθ)/∣sinθ∣
=2/∣sinθ∣
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