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verify that the equation is an identity:

(1-cosX)/(1+cosX) = (cscX-cotX)^2

  • Math -

    LS = (1- cosx)/(1 + cosx) [(1-cox)/(1-cosx)]
    = (1-cosx)^2/(1-cos^2x)

    RS = (1/sinx - cosx/sinx)^2
    = ((1-cosx)/sinx)^2
    = (1-cosx)^2 /(sin^2x)
    = (1-cosx)^2/(1-cos^2)
    = LS

  • Math -

    thanks. How would you know how to do similar problems? Where should i start when verifying trig equations?

  • Math -

    Usually start with the complicated looking side and try to reduce to the simpler side.

    In this case I worked on both sides.
    Also I often change everything to sines and cosines, unless I recognize a popular identity.

    How did I know where to start??

    Let's say doing this for 35 years and doing thousands of these could be the reason, lol

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