Question

已知sinθ+cosθ=1/3,求tanθ+1/tanθ的值

Answer 1

已知两边平方得到：
1+2sinθcosθ=1/9
所以：sinθcosθ=-4/9.
tanθ+1/tanv
=sinθ/cosθ+cosθ/sinθ
=(sin^2θ+cos^2θ)/(sinθcosθ)
=1/(sinθcosθ)
=-9/4.

Answer 2

∵sinθ+cosθ=1/3 sin^2θ+cos^2θ=1
∴sinθcosθ=-4/9
∴tanθ+1/tanθ=（sin^2θ+cos^2)/cosθsinθ=1/cosθsinθ=-9/4

Answer 3

(sinθ+cosθ)^2=1+2*sinθ*cosθ=1/9
sinθ*cosθ=-4/9
tanθ+1/tanθ=sinθ/cosθ+cosθ/sinθ=1/(sinθ*cosθ)=-9/4