How do you prove the identity $(1-sinx)/cosx=cosx/(1+sinx)$ ?

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Answer 1 · 2016-10-15T12:32:42

By multiplying both numerator and denominator by $1+sinx$ and using the difference of squares the result follows quickly.

multiply the LHS , top and bottom by $(1+sinx)$

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

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

but $sin^2x+cos^x=1$

$:. =(cos^2x)/(cosx(1+sinx))$

$=(cancel(cosx)(cosx))/(cancelcosx(1+sinx))$

as required.

How do you prove the identity (1-sinx)/cosx=cosx/(1+sinx)(1-sinx)/cosx=cosx/(1+sinx)?