Tan^2= csc^2 tan^2 -1

see my previous comment about trig names

RS = csc^2 Ø tan^2 Ø - 1
= 1/sin^2 Ø(sin^2 Ø/cos^2 Ø) - 1
= 1/cos^2 Ø - cos^2 Ø/cos^2 Ø
= (1 - cos^2)/cos^2 Ø
= sin^2 Ø/cos^2 Ø
= tan^2 Ø
= LS