SOLUTION: what is the exact value od tangent 75 Degrees? so far i had: tan (45+30) tan45+tan30 ___________ 1-tan45+tan30 but im not sure what to do after that.

Algebra ->  Trigonometry-basics -> SOLUTION: what is the exact value od tangent 75 Degrees? so far i had: tan (45+30) tan45+tan30 ___________ 1-tan45+tan30 but im not sure what to do after that.      Log On


   

Question 249327: what is the exact value od tangent 75 Degrees?
so far i had: tan (45+30)
tan45+tan30
___________
1-tan45+tan30
but im not sure what to do after that.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
From here, use the unit circle:




Recall that tan%28x%29=sin%28x%29%2Fcos%28x%29. So tan%2845%29=sin%2845%29%2Fcos%2845%29=%28sqrt%282%29%2F2%29%2F%28sqrt%282%29%2F2%29=1 and tan%2830%29=sin%2830%29%2Fcos%2830%29=%281%2F2%29%2F%28sqrt%283%29%2F2%29=1%2Fsqrt%283%29


In short, we have tan%2845%29=1 and tan%2830%29=1%2Fsqrt%283%29


Simply plug these values into %28tan%2845%29%2Btan%2830%29%29%2F%281-tan%2845%29%2Atan%2830%29%29 to find tan%2845%2B30%29


Note: your answer should be tan%2875%29=%28sqrt%283%29%2B1%29%2F%28sqrt%283%29-1%29