Trig Identities

Prove the following identities:
13. tan(x) + sec(x) = (cos(x)) / (1-sin(x))

*Sorry for any confusing parenthesis.*

My work:
I simplified the left side to
a. ((sinx) / (cosx)) + (1 / cosx) , then
b. (sinx + 1) / cosx = (cos(x)) / (1-sin(x))

I don't know how to verify the rest.

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  1. good start

    LS = sinx/cosx + 1/cosx
    = (sinx + 1)/cosx
    multiply top and bottom by (sinx - 1)/(sinx - 1)
    = (sinx + 1)/cosx * (sinx - 1)/(sinx - 1)
    = (sin^2 x - 1)/(cosx(sinx - 1))
    = cos^2 x/(cosx(sinx - 1))
    = cosx/(sinx - 1)
    = RS

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  2. Thank you so much! I understand it now.

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