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PreCalculus (PLEASE HELP, IM BEGGING!)

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Can anyone please explain these problems to me?? I really need help!I need to simplify these trig expressions but I don't understand how my teacher is doing it at all and I have a quiz on this tomorrow! I've really been trying but I just don't get it!

1)Mulitply:
[cosx/(1-cosx)][1+sinx/(1+sinx)]

2)Rewrite over common denominator:
[1/(1-cosx)]+[1/(1+cosx)]

3)Establish the identity:
[(1-cot^2x)/(1+cot^2x)]+1=2sin^2x

  • PreCalculus (PLEASE HELP, IM BEGGING!) -

    cos/(1-cos) * ((1+sin)+sin)/(1+sin)

    cos(1+2sin)/((1-cos)(1+sin))
    Not sure how to make it any simpler. No chance of a typo in the problem?

    ----------------------------

    ((1+cos) + (1-cos))/(1-cos)(1+cos)

    2/sin^2

    ----------------------

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

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

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

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

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