同角三角函数的关系化简1,（cosθ/sinθ）^2-1/sin^θ2,sin^4θ-cos^4θ3,cotx+tanx/csc^x

Question

同角三角函数的关系
化简
1,（cosθ/sinθ）^2-1/sin^θ
2,sin^4θ-cos^4θ
3,cotx+tanx/csc^x

Answer 1

1、（cosθ/sinθ）^2-1/sin^4θ
=（cosθ/sinθ）^2-(sin^2θ+cos^2θ)/sin^4θ
=（cosθ/sinθ）^2-1/sin^2θ-cos^2θ/sin^4θ
=（cos^2θ-1）/sin^2θ-cos^2θ/sin^4θ
=-1-cos^2θ/sin^4θ
应该可以再化,我不会了.
2、sin^4θ-cos^4θ

=(sin^2θ-cos^2θ)(sin^2θ+cos^2θ)
=sin^2θ-cos^2θ
=1-2sin^2θ(或=2sin^2θ-1)
3、“csc^x”是?
cotx=1/tanx=cosx/sinx,tanx=sinx/cosx,cscx=1/cosx（你自己化一下啰）