trig

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

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  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

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