prove identities(f.2 maths)20點

1.
tan^2θ-1/cos^2θ
=sin^2θ/cos^2θ-1/cos^2θ
=(sin^2θ-1)/cos^2θ
=-cos^2θ/cos^2θ
=-1

2.
tanθ+1/tanθ
=sinθ/cosθ+cosθ/sinθ
=sin^2θ+cos^2θ/sinθcosθ
=1/sinθcosθ
=1/sinθsin(90-θ)

3.
sin^2θ/tan^2θ
=sin^2θ/(sin^2θ/cos^2θ)
=cos^2θ
=1-sin^2θ
=1-cos^2(90-θ)

4.
(cosθ-sinθ)^2
=cos^2θ-2sinθcosθ+sin^2θ
=(cos^2θ+sin^2θ)-2sinθcosθ
=1-2sinθcosθ