How do you evaluate $tan (120)$ $tan (120)$ ?

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Answer 1 · 2015-11-29T21:49:31

Evaluate tan (120)
Ans: $- \sqrt{3}$ $- sqrt3$

Trig table of special arcs --> $tan 120 = - \sqrt{3}$ $tan 120 = -sqrt3$
$tan 120 = tan (150 - 30) = (\frac{tan (150 - tan 30)}{1 + tan 30 . tan .60} =$ $tan 120 = tan (150 - 30) = (tan (150 - tan 30)/(1 + tan 30.tan.60) =$
$= \frac{- \frac{\sqrt{3}}{3} - \frac{\sqrt{3}}{3}}{1 + (- \frac{\sqrt{3}}{3}) (\frac{\sqrt{3}}{3})} =$ $= (-sqrt3/3 - sqrt3/3)/[1 + (-sqrt3/3)(sqrt3/3)] =$
$= \frac{(- 2) (\frac{\sqrt{3}}{3})}{(1 - \frac{1}{3})} = (\frac{- 2 \sqrt{3}}{3}) (\frac{3}{2}) = - \sqrt{3}$ $= ((-2)(sqrt3/3))/((1 - 1/3)) = ((-2sqrt3)/3)(3/2) = -sqrt3$

How do you evaluate tan(120)tan (120)?