sinΘ-cosΘ=1/2,求tanΘ+cotΘ

问题描述:

sinΘ-cosΘ=1/2,求tanΘ+cotΘ

解sinθ-cosθ=1/2两边平方得:sin²θ-2sinθcosθ+cos²θ=1/4即1-2sinθcosθ=1/4∴sinθcosθ=3/8∴tanθ+cotθ=(sinθ/cosθ)+(cosθ/sinθ)=(sin²θ+cos²θ)/(sinθcosθ)=1/(3/8)=8/3...