(tanx+cotx)over(tanx-cotx)=(1) over sin^2x-cos^2x)

Answer 1

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