SOLUTION: 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.

Algebra ->  Trigonometry-basics -> SOLUTION: 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.      Log On


   

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.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:



and express the answer in terms of tan%28theta%29

..........common denominator









%284cos%28theta%29sin%28theta%29%29%2F%28cos%5E2%28theta%29-sin%5E2%28theta%29%29.....use identity cos%5E2%28theta%29=1-sin%5E2%28theta%29

%284cos%28theta%29sin%28theta%29%29%2F%281-sin%5E2%28theta%29-sin%5E2%28theta%29%29

%284cos%28theta%29sin%28theta%29%29%2F%281-2sin%5E2%28theta%29%29........Double-Angle Identities +2cos%28theta%29sin%28theta%29=sin%282theta%29 and 1-2sin%5E2%28theta%29=cos%282theta%29+

%282sin%282theta%29%29%2Fcos%282theta%29+

2tan%282theta%29


Answer by ikleyn(52909) About Me  (Show Source):
You can put this solution on YOUR website!
.
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. 


..........common denominator














%284cos%28theta%29sin%28theta%29%29%2F%28cos%5E2%28theta%29-sin%5E2%28theta%29%29.....divide the numerator and the denominator by cos%5E2%28theta%29


%284tan%28theta%29%29%2F%281-tan%5E2%28theta%29%29      ANSWER

Solved and answered, as requested.