SOLUTION: Simplify the expression into one trigonometric function then evaluate if possible. Tan(-285)

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify the expression into one trigonometric function then evaluate if possible. Tan(-285)      Log On


   

Question 1005072: Simplify the expression into one trigonometric function then evaluate if possible.
Tan(-285)
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
tan(-285) = tan(-105) = tan(75) = tan(45 + 30) =
(tan(45) + tan(30)) /(1 - tan(45)*tan(30)) =
%281+%2B+sqrt%283%29%2F3%29+%2F+%281+-+sqrt%283%29%2F3%29 =
Now multiply top and bottom by 1 + sqrt(3)/3 and get
(1 + 2(sqrt(3)/3) + 1/3) / (1 - 1/3) =
(1 + 2(sqrt(3)/3) + 1/3) / (2/3) =
(3/2)(1 + 2(sqrt(3)/3) + 1/3) =
3/2 + sqrt(3) + 1/2 =
2 + sqrt(3)