SOLUTION: what is the exact value of tan(15degrees)?

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Question 584627: what is the exact value of tan(15degrees)?
Answer by lwsshak3(11628) About Me  (Show Source):
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what is the exact value of tan(15degrees)
tan(15º)=tan(60-45)
Using tan addition formula:
tan (60-45)=(tan60-tan45)/(1+tan60*tan45)
=(√3-1)/(1+√3*1)
=(√3-1)/(√3+1)
rationalize by multiplying top and bottom by (√3-1)
=(√3-1)^2/(3-1)
=(3-2√3+1)/2
=(4-2√3)/2=2-√3
tan15º=2-√3