There are two questions of my homework I'm having trouble with.. I think we are supposed to show how they are true. In other words, make one side look exactly like the other one by using the identities.

1. cosX/(1-sinX)=(1+sinX)/cosX

2. (secX+tanX)/(secX-tanX)=(1+2sinX+sin^(2)X)/cos^(2)X)

Please help, thanks

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  1. for the first, multiply the LS by (1+sinx)/(1+sinx)
    It will turn into the RS

    LS = (1/cosx + sinx/cosx)/(1/cosx - sinx/cosx)
    we have a common denominator
    and remember how to divide fractions ...

    = (1+sinx)/(1-sinx)

    RS = (1+sinx)(1+sinx)/(1 - sin^2 x)
    = (1+sinx)(1+sinx)/[(1+sinx)(1+sinx)]
    = (1+sinx)/(1-sinx)
    = LS

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  2. Thanks!

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