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Question 151392: tan(pi/6 + pi/4): tan(pi/6 + pi/4)
Answer by jim_thompson5910(9390) About Me  (Show Source):
You can put this solution on YOUR website!
tan(pi/6 + pi/4) Start with the given expression.


(tan(pi/6) + tan(pi/4))/(1-tan(pi/6)tan(pi/4)) Use the identity tan(A + B)=(tan(A) + tan(B))/(1-tan(A)tan(B)) to expand the expression.



(sqrt(3)/3 + 1)/(1-(sqrt(3)/3)(1)) Using the unit circle, evaluate tan(pi/6) to get sqrt(3)/3 and evaluate tan(pi/4) to get 1


(sqrt(3)/3 + 1)/(1-sqrt(3)/3) Multiply


((sqrt(3)+3)/3)/((3-sqrt(3))/3) Combine the fractions.


((sqrt(3)+3)/3)(3/(3-sqrt(3)))Multiply the first fraction by the reciprocal of the second fraction.


((sqrt(3)+3)/cross(3))(cross(3)/(3-sqrt(3))) Cancel out the common terms.


(sqrt(3)+3)/(3-sqrt(3)) Simplify.


((sqrt(3)+3)/(3-sqrt(3)))((3+sqrt(3))/(3+sqrt(3))) Multiply the fraction by (3+sqrt(3))/(3+sqrt(3))


((sqrt(3)+3)(3+sqrt(3)))/((3+sqrt(3))(3-sqrt(3))) Combine the fractions.


(3*sqrt(3)+3+9+3*sqrt(3))/(6) FOIL


(6*sqrt(3)+12)/(6) Combine like terms


(6(sqrt(3)+2))/(6) Factor out the GCF 6


sqrt(3)+2 Reduce



So tan(pi/6 + pi/4)=sqrt(3)+2