求几道高一三角函数的题~~

1.
(cosA-sinA)^2=cos^2A+sin^2A-2sinA*cosA=1+1/4=5/4
又有sinA*cosA=-1/8<0，π/2<A<π
cosA-sinA=-根号5/2
2.
sinθ=1-sin^2θ=cos^2θ
cos^2θ+cos^4θ=sinθ+sin^2θ=1
3.
(sinθ-cosθ)^2=cos^2θ+sin^2θ-2sinθ*cosθ=1+120/169=289/169
由0<θ<π，sinθ*cosθ=-60/169<0
π/2<θ<π
sinθ-cosθ=17/13
4.
0<θ<π
(sinθ+cosθ)^2=cos^2θ+sin^2θ+2sinθ*cosθ=1+2sinθ*cosθ=1/25
sinθ*cosθ=-12/25<0
故π/2<θ<π
sinθ>0，cosθ<0
(sinθ-cosθ)^2=cos^2θ+sin^2θ-2sinθ*cosθ=49/25
sinθ-cosθ=7/5
可得sinθ=4/5
cosθ=-3/5
tanθ=-4/3
5.
由韦达定理
sinθ+cosθ=-(根号2+1)/2
sinθ*cosθ=5m/2
(sinθ+cosθ)^2=cos^2θ+sin^2θ+2sinθ*cosθ=1+5m=(3+2根号2)/4
m=(2根号2-1)/20
sinθ/(1-cotθ)+cosθ/(1-tanθ)
=sin^2θ/(sinθ-cosθ)+cos^2θ/(cosθ-sinθ)
=(sin^2θ-cos^2θ)/(sinθ-cosθ)
=sinθ+cosθ
=1/5


6、7两题比较麻烦，不想算了……

回复：10楼
笔误了，答案是-(根号2+1)/2

抽出了一点时间，帮你做了一下6、7两题……
6.
sin^2(A)+cos^2(A)*sin^2(B)*cos^2(C)=sin^2(B)
sin^2(A)+cos^2(A)*sin^2(B)*(1-sin^2(C))=sin^2(B)
sin^2(A)+(cos^2(A)-1)*sin^2(B)=sin^2(B)*sin^2(C)*cos^2(A)
sin^2(A)-sin^2(A)*sin^2(B)=sin^2(B)*sin^2(C)*cos^2(A)
sin^2(A)*(1-sin^2(B))=sin^2(B)*sin^2(C)*cos^2(A)
sin^2(A)*cos^2(B)=sin^2(B)*sin^2(C)*cos^2(A)
tan^2(A)=tan^2(B)*sin^2(C)
7.
1-cosα=sinθ*sinα
1+cosα=tanθ*sinα
1-cos^2α=sin^2α*tanθ*sinθ
tanθ*sinθ=sin^2θ/cosθ=1
sin^2θ/cosθ=(1-cos^2θ)/cosθ=1/cosθ-cosθ
cosθ-1/cosθ=-1

sin^2(A)+cos^2(A)*sin^2(B)*(1-sin^2(C))=sin^2(B)
sin^2(A)+sin^2(B)*(cos^2(A)-1-cos^2(A)*sin^2(C))=0
sin^2(A)+sin^2(B)*sin^2(A)=sin^2(B)*sin^2(C)*cos^2(A)