SOLUTION: Verify the identity. Justify each step. tan theta + cot theta = 1/sin theta cos theta

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the identity. Justify each step. tan theta + cot theta = 1/sin theta cos theta      Log On


   

Question 627972: Verify the identity. Justify each step.
tan theta + cot theta = 1/sin theta cos theta
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Since tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 and cot%28theta%29=cos%28theta%29%2Fsin%28theta%29 ,

For a common denominator to add those two fractions, the obvious choice is sin%28theta%29cos%28theta%29 , so

Now we can write it all as one fraction:

At this point, you can use the identity sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1 to conclude that
tan%28theta%29%2Bcot%28theta%29=1%2Fsin%28theta%29cos%28theta%29