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Question
Tan(5Pi/12) using Sum or difference Identities
tan(5pi/12)
tan((pi/6) + (pi/4))
tan(x + y) = (tan(x) + tan(y))/(1 - tan(x)tan(y))
tan((pi/6)+(pi/4)) = (tan(pi/6)+tan(pi/4))/(1 - tan(pi/6)tan(pi/4))
tan(5pi/12) = ((sqrt(3)/3) + 1)/(1 - (sqrt(3)/3)(1))
tan(5pi/12) = ((sqrt(3) + 3)/3) / ((3 - sqrt(3))/3)
tan(5pi/12) = (3 + sqrt(3))/(3 - sqrt(3))
multiply top and bottom by 3 + sqrt(3) to get rid of the sqrt
tan(5pi/12) = (9 + 6sqrt(3) + 3)/(9 - 3)
tan(5pi/12) = (12 + 6sqrt(3))/6
tan(5pi/12) = (6(2 + sqrt(3)))/6
ANS : tan(5pi/12) = 2 + sqrt(3)
more info found at http://math2.org/math/trig/identities.htm
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