Prove that sin^2(Omega) - Cos^2(Omega) / tan(Omega) sin(Omega) + cos(Omega) tan(Omega) = cos(Omega) - cot (Omega) cos (omega)

Answer 1

I substituted any angle in the equation the way you typed it, and the equation was false.
I then tried it as

(sin^2 Ø - cos^2 Ø)/(tanØsinØ + cosØtanØ)

using Ø instead of omega for easier typing.

and got
LS = (sinØ+cosØ)(sinØ-cosØ)/(tanØ(sinØ+cosØ)
= (sinØ - cosØ)/(sinØ/cosØ)
= cosØ(sinØ - cosØ)/sinØ
= cosØsinØ/sinØ - cos^2 Ø/sinØ
= cosØ - (cosØ/sinØ)cos‚
= cosØ - cotØcosØ
= RS

Answer 2

What does LS and RS stand for?