Question 1178040
.
Simplify:   [cos⁡θ+sin⁡θ]/[cos⁡θ-sin⁡θ] -[cos⁡θ-sin⁡θ]/[cos⁡θ+sin⁡θ] and express the answer in terms of tan⁡θ.
~~~~~~~~~~~~~~~~~~~



            The problem requests to express the answer in terms of tan⁡θ,

            so I came to do it as requested.



<pre>
{{{ (cos(theta)+sin(theta))/(cos(theta)-sin(theta))-(cos(theta)-sin(theta))/(cos(theta)+sin(theta))}}}..........common denominator{{{ (cos(theta)-sin(theta))(cos(theta)+sin(theta))=(cos^2(theta)-sin^2(theta))}}}


{{{((cos(theta)+sin(theta))(cos(theta)+sin(theta)) -(cos(theta)-sin(theta))(cos(theta)-sin(theta)))/(cos^2(theta)-sin^2(theta))}}}


{{{((cos(theta)+sin(theta))^2 -(cos(theta)-sin(theta))^2)/(cos^2(theta)-sin^2(theta))}}}


{{{((cos^2(theta)+2cos(theta)sin(theta)+sin^2(theta))-(cos^2(theta)-2cos(theta)sin(theta)+sin^2(theta)))/(cos^2(theta)-sin^2(theta))}}}


{{{(cos^2(theta)+2cos(theta)sin(theta)+sin^2(theta)-cos^2(theta)+2cos(theta)sin(theta)-sin^2(theta))/(cos^2(theta)-sin^2(theta))}}}


{{{(4cos(theta)sin(theta))/(cos^2(theta)-sin^2(theta))}}}.....divide the numerator and the denominator by {{{cos^2(theta)}}}


{{{(4tan(theta))/(1-tan^2(theta))}}}      <U>ANSWER</U>
</pre>

Solved and answered, as requested.