1.) Simplify tan2 θ(1 – cot2 θ). Math

2.) Simplify sin2 θ(1 – csc2 θ).
This math totally confuses me and I take cyber school so I don't have anyone to help me. Thanks.

1. tan2 θ(1 – cot2 θ)

= tan2 θ – tan2θ *cot2 θ

= tan2 θ – 1

2. sin2 θ(1 – csc2 θ).

= sin2 θ – sin2 θ *csc2 θ

= sin2 θ – 1

It is exactly like this;-

1. tan(2θ){1 - cosec(2θ)}

= tan(2θ) - {sin(2θ)/cos(2θ)}{1/sin(2θ)}

= tan(2θ) - {1/cos(2θ)}

= {sin(2θ) - 1}/cos(2θ)

= -{sin^2 θ + cos^2 θ - 2sinθcosθ}/((cosθ - sinθ)(cosθ + sinθ)

= (sinθ - cosθ)/(sinθ + cosθ)

2. sin2 θ(1 – cosec2 θ)

= sin2θ - 1

= - { sin^2 θ + cos^2 θ - 2sinθcosθ}

= - (sinθ - cosθ)^2 .