SOLUTION: 2 tan 30°÷1+tan² 30=?

Algebra ->  Trigonometry-basics -> SOLUTION: 2 tan 30°÷1+tan² 30=?      Log On


   

Question 977146: 2 tan 30°÷1+tan² 30=?
Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
%282tan%2830%29%29%2F%281%2Btan%5E2%2830%29%29
We have the identity
%281%2Btan%5E2%28x%29%29=sec%5E2%28x%29
and substitute
%282tan%2830%29%29%2F%28sec%5E2%2830%29%29
We know that tan%28x%29=sin%28x%29%2Fcos%28x%29 and that sec%28x%29=%281%2Fcos%28x%29%29 and after substituting, we have
2sin%2830%29cos%2830%29
sin%2830%29=1%2F2 and cos%2830%29=sqrt%283%29%2F2%29
%28sqrt%283%29%29%2F4