3 years ago
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value.
(tan (pi)/(18)+tan (pi)/(9))/(1-tan (pi)/(18)tan (pi)/(9))
1 Answers
Best Answer
davidspadeconcertnewjersey Staff answered 3 years ago
davidspadeconcertnewjersey Staff answered 3 years ago
The expression can be expressed as the tangent of the sum of the angles (pi)/(18) and (pi)/(9) because according to the Addition formula for Tangents, tan(alpha + beta)=(tan alpha + tan beta)/(1-tan alpha tan beta) where alpha = (pi)/(18) and beta = (pi)/(9).
We recall that
tan (pi)/(6)=(sqrt(3))/(3).
(tan (pi)/(18)+tan (pi)/(9))/(1-tan (pi)/(18) tan (pi)/(9))=tan ((pi)/(18)+(pi)/(9))
=tan (pi)/(6)
=(sqrt(3))/(3)
Result:
(sqrt(3))/(3)