(cosx) / 1 + sinx

=

(1-sinx) / cos x

Multiply the top and bottom by 1+sinx, you get: cosx(1+sinx) / (1-sinx)(1+sinx) The denominator using (a+b) (a-b)=a^2-b^2 what you have now is cosx(1+sinx) / 1-sin^x You know that 1-sin^x is equal to cos^x so know you have cosx(1+sinx) / cos^x get rid of the cosx on top by simplifying and the cos^x so that you're left with (1+sinx) / cos x Therefore cosx / 1- sinx = 1 + sinx / cos x

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