Math

So I found the derivative of an expression and I cannot figure out how to simplify the final answer into the desired form. I got -csc^2(X)/(1+cotx)^2. Now how do I simplify this into -1/(sinx+cosx)^2. Help, it's killing me ahha. Thanks!

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  1. - 1/sin^2
    ---------------
    (1 + cos/sin)^2

    -1
    ------------------------------
    sin^2 [ (1+cos/sin)(1+cos/sin)]

    -1
    --------------------------
    (sin+cos)(sin+cos)

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