sinΘ-cosΘ=1/2,求tanΘ+cotΘ

sinΘ-cosΘ=1/2,求tanΘ+cotΘ

解sinθ-cosθ=1/2兩邊平方得:sin²;θ-2sinθcosθ+cos²;θ=1/4即1-2sinθcosθ=1/4∴sinθcosθ=3/8∴tanθ+cotθ=(sinθ/cosθ)+(cosθ/sinθ)=(sin²;θ+cos²;θ)/(sinθcosθ)=1/(3/8)=8/3…