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26 January, 16:45

Verify the identity:

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

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  1. 26 January, 17:07
    0
    For the answer to the question above,

    Let's work with the left-hand side

    We're going to times cosx/1-sinx by 1+sinx/1+sinx, you can do this because 1+sinx/1+sinx is equal to 1, so you aren't really changing anything.

    After you've times the top and bottom by 1+sinx, you get:

    cosx (1+sinx) / (1-sinx) (1+sinx)

    The denominator is a difference of squares, so you get 1-sin^2 x

    what you have now is

    cosx (1+sinx) / 1-sin^2x

    You know that 1-sin^2x is equal to cos^2x

    so know you have

    cosx (1+sinx) / cos^2x

    get rid of the cosx on top by simplifying and the cos^2x so that you're left with

    (1+sinx) / cos x

    Therefore cosx / 1 - sinx = 1 + sinx / cos x
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