Question

若 (sinθ+cosθ)/(sinθ-cosθ)=2,则sinθ×cosθ=?

Answer 1

解：
由：(sinθ+cosθ)/(sinθ-cosθ)=2
得：(tanθ+1)/(tanθ-1)=2
得：tanθ=3
所以：(secθ)^2=1+(tanθ)^2=10
所以：(cosθ)^2=1/(secθ)^2=1/10
所以，原式=tanθ×(cosθ)^2=3/10

Answer 2

sinθ-cosθ=1/2
(sinθ-cosθ)^2=1/4
1-2sinθcosθ=1/4
sinθcosθ=3/8
sin^3θ-cos^3θ
=(sinθ-cosθ)(sin^2θ+sinθcosθ+cos^2θ)
=(1+sinθcosθ)/2
=(1+3/8)/2
=11/16

Answer 3

(sinθ+cosθ)/(sinθ-cosθ)=2则
(sinθ+cosθ)²/(sinθ-cosθ)²=4
（1+2sinθcosθ）/(1-2sinθcosθ)=4
解得sinθcosθ=3/10
这样说不知道是否清楚

Answer 4

(sinθ+cosθ)/(sinθ-cosθ)=2
(sinθ+cosθ)=2(sinθ-cosθ)
1+2sinθcosθ=4(1-2sinθcosθ)=4-8sinθcosθ
sinθcosθ=3/10