SOLUTION: find the exact value by using a sum or difference identity tan(pi/12)

Question 766924: find the exact value by using a sum or difference identity
tan(pi/12)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the exact value by using a sum or difference identity
tan(pi/12)
--
1/12 = 1/3 - 1/4
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tan(pi/12) = tan[pi/3 - pi/4) = [tan(pi/3)-tan(pi/4)]/[1+tan(pi/3)tan(pi/4]
------
= [sqrt(3)-1]/[1+sqrt(3)]
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={(sqrt(3)-1)(sqrt(3)-1)]/[sqrt(3)+1]^2
----
= [3-2sqrt(3)+1]/[3-1]
------------------------------
= [4-2sqrt(3)]/2
-----
= 2-sqrt(3)
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Cheers,
Stan H.
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