trig
posted by stacey graham on .
(tanx+cotx)over(tanxcotx)=(1) over sin^2xcos^2x)

Writing everything in terms of sine and cosine usually works, so ...
LS = (sinx/cosx + cosx/sinx)/(sinx/cosx  cosx/sinx)
= [(sin^2x + cos^2x)/sinxcosx]/[(sin^2x  cos^2x)/(sinxcosx)]
= [(sin^2x + cos^2x)/sinxcosx][(sinxcosx0)/(sin^2x  cos^2x)]
= 1/(sin^2x  cos^2x)
= RS