I need to prove that the following is true. Thanks

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

I recall this question causing all kinds of problems when I was still teaching.

it requires a little "trick"

L.S.
=cosx/(1-sinx) multiply top and bottom by 1+sinx, (creating the difference of square pattern)
=cosx(1+sinx)/[(1-sinx)(1+sinx)]
=cosx(1+sinx)/(1-sin^2x)
=cosx(1+sinx)/cos^2x divide by cosx
= (1+sinx)/cosx
= R.S.

Wow !!

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