SOLUTION: tan(pi/6 + pi/4)

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Question 151392: tan(pi/6 + pi/4)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28pi%2F6+%2B+pi%2F4%29 Start with the given expression.


%28tan%28pi%2F6%29+%2B+tan%28pi%2F4%29%29%2F%281-tan%28pi%2F6%29tan%28pi%2F4%29%29 Use the identity tan%28A+%2B+B%29=%28tan%28A%29+%2B+tan%28B%29%29%2F%281-tan%28A%29tan%28B%29%29 to expand the expression.



%28sqrt%283%29%2F3+%2B+1%29%2F%281-%28sqrt%283%29%2F3%29%281%29%29 Using the unit circle, evaluate tan%28pi%2F6%29 to get sqrt%283%29%2F3 and evaluate tan%28pi%2F4%29 to get 1


%28sqrt%283%29%2F3+%2B+1%29%2F%281-sqrt%283%29%2F3%29 Multiply


%28%28sqrt%283%29%2B3%29%2F3%29%2F%28%283-sqrt%283%29%29%2F3%29 Combine the fractions.


%28%28sqrt%283%29%2B3%29%2F3%29%283%2F%283-sqrt%283%29%29%29Multiply the first fraction by the reciprocal of the second fraction.


%28%28sqrt%283%29%2B3%29%2Fcross%283%29%29%28cross%283%29%2F%283-sqrt%283%29%29%29 Cancel out the common terms.


%28sqrt%283%29%2B3%29%2F%283-sqrt%283%29%29 Simplify.


Multiply the fraction by %283%2Bsqrt%283%29%29%2F%283%2Bsqrt%283%29%29


Combine the fractions.


%283%2Asqrt%283%29%2B3%2B9%2B3%2Asqrt%283%29%29%2F%286%29 FOIL


%286%2Asqrt%283%29%2B12%29%2F%286%29 Combine like terms


%286%28sqrt%283%29%2B2%29%29%2F%286%29 Factor out the GCF 6


sqrt%283%29%2B2 Reduce



So tan%28pi%2F6+%2B+pi%2F4%29=sqrt%283%29%2B2