Question

已知sin(α+π/4)+sin(α-π/4)=根号2/3 则sin(α-π/4)/1-cos2α-sin2α的值为

要详细过程
已知sin(α+π/4)+sin(α-π/4)=根号2/3 则sin(α-π/4)/1-cos2α-sin2α的值为

Answer 1

解由sin(α+π/4)+sin(α-π/4)=√2/3

即sinacosπ/4+cosasinπ+sinacosπ/4-cosasinπ=√2/3
即2sinacosπ/4=√2/3
即sina=1/3
故sin(α-π/4)/1-cos2α-sin2α
=sin(α-π/4)/[1-(1-2sin^2α)-sin2α]
=sin(α-π/4)/[2sin^2α-2sinαcosa]
=(sinacosπ/4-cosasinπ)/[2sin^2α-2sinαcosa]
=√2/2(sina-cosa)/2sina(sina-cosa)
=√2/4×1/sina
=√2/4×1/(1/3)
=3√2/4

Answer 2

能在后面的式子中加上括号吗，不然不清楚哪些项是一起的

追问

sin(α-π/4)与
1-cos2α-sin2α
是分开的