Trigonometry

[sinxcosx/(1+cosx(]-[sinx/(1-cosx)]= -(cotxcosx+cscx)

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  1. multiply top and bottom of the left most by
    (1-cos x)
    multiply top and bottom of the second term on the left by (1 + cos x)
    that gives you the common denominator on the left of (1 - cos^2 x) which is sin^2 x

    then do the two multiplications on the top to get on the top
    sin x cos x - sin x cos^2 x
    and
    - (sin x + cos x sin x)
    combine for a numerator of
    sin x cos x- sin x cos^2 x - sin x - sin x cos x
    simplify and divide top and bottom by sin x
    [- cos^2 x - 1]/sin x on the left

    now work on the right
    cot x = cos x/ sin x
    so
    - (cos^2 x / sin x + 1/sin x)
    which is what you have on the left

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    posted by Damon

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