Question

Verify the identity and show all steps.
(1+tanx)/(1-tanx)=(cosx+sinx)/(cosx-sinx)

Answer 1

If the equation is true then the LHS - RHS is equal to zero.

Move the RHS to the LHS and combine the terms. In the numerator you will have the following expression:\[(\text{Cos}[x]-\text{Sin}[x] \text{Tan}[x])-(\text{Cos}[x]-\text{Sin}[x] \text{Tan}[x]) \]The sum of the above is zero.