1/cosθ-1/sinθ=1
(sinθ-cosθ)/sinθcosθ=1
sinθ-cosθ=sinθcosθ
两边平方
1-2sinθcosθ=(sinθcosθ)^2
(sinθcosθ)^2+2sinθcosθ-1=0
(sinθcosθ+1)^2=2
sinθcosθ=正负√2 -1
sin2θ=2sinθcosθ=正负2√2 -2