Question 438731: Addition or subtraction formula to find the exact value
tan(7pi/12)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Addition or subtraction formula to find the exact value
tan(7pi/12)
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Addition formula for tan:
tan(x+y)=(tanx+tany)/(1-tanxtany)
let x=3pi/12=pi/4
let y=4pi/12=pi/3
tan(7pi/12 is in Quadrant II, therefore, it is negative.
tanx=tan pi/4=1
tany=tan pi/3=sqrt(3)
tan(7pi/12)=tan(pi/4+pi/3)=(1+sqrt(3))/(1-sqrt(3))
(1+sqrt(3)(1+sqrt(3)/(1+sqrt(3)(1-sqrt(3)
(1+2sqrt(3)+3)/1-3
(4+2sqrt(3))/-2
-(2+sqrt(3))
ans:
tan(7pi/12)=-(2+sqrt(3))
note: you could also use the half-angle formula for tan to solve, which might be easier.
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