SOLUTION: Verify that tan theta/ sec theta= sin theta

Algebra ->  Trigonometry-basics -> SOLUTION: Verify that tan theta/ sec theta= sin theta      Log On


   

Question 709264: Verify that tan theta/ sec theta= sin theta
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
When you are not sure how to prove a Trig identity (like this), it can be helpful to convert any tan's, cot's, sec's and/or csc's into equivalent expressions in terms of of sin and/or cos.

With tan = sin/cos and sec = 1/cos your equation becomes:
%28sin%28theta%29%2Fcos%28theta%29%29%2F%281%2Fcos%28theta%29%29+=+sin%28theta%29
We can simplify the fractions within a fraction on the left side bu multiplying the numerator and denominator of the "big" fraction by cos%28theta%29:

The cos's cancel:

leaving:
%28sin%28theta%29%2F1%29%2F%281%2F1%29%29+=+sin%28theta%29
which simplifies to:
sin%28theta%29+=+sin%28theta%29
And we're finished!