How do you verify (1+tanx)/(1-tanx) = (cosx+sinx)/(cosx-sinx)?

1 Answer
Jim G.
Mar 9, 2016

see explanation

Explanation:

manipulate the left side

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

rewrite numerator / denominator as single fractions.

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

multiply the fractions by ' inverting' the fraction on denominator.

rArr (cosx+sinx)/cancel(cosx) xx (cancel(cosx))/(cosx-sinx)

= (cosx+sinx)/(cosx-sinx) = " right side "

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