SOLUTION: Evaluate {{{ tan(pi/6 - pi/3) }}} I got up to {{{(sqrt ( 3 )/3 + sqrt ( 3 ))/2}}} Regards, Peter

Algebra ->  Trigonometry-basics -> SOLUTION: Evaluate {{{ tan(pi/6 - pi/3) }}} I got up to {{{(sqrt ( 3 )/3 + sqrt ( 3 ))/2}}} Regards, Peter      Log On


   

Question 1054317: Evaluate +tan%28pi%2F6+-+pi%2F3%29+
I got up to %28sqrt+%28+3+%29%2F3+%2B+sqrt+%28+3+%29%29%2F2
Regards, Peter
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Basic Identity for this Tangent expression:
tan%28x-y%29=%28tan%28x%29-tan%28y%29%29%2F%281%2Btan%28x%29tan%28y%29%29

Using reference angles and Unit Circle,
system%28tan%28pi%2F6%29=sqrt%283%29%2F3%2Ctan%28pi%2F3%29=sqrt%283%29%29


You made a mistake in sign. Your expression should really be %28sqrt%283%29%2F3-sqrt%283%29%29%2F2
.

From that, and that you're studying Trigonometry, your arithmetic steps should bring the simplification to -sqrt%283%29%2F3.