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answer is -2 - sqrt(3)

tan(7pi/12)=sin(7pi/6)/(1+cos(7pi/6))
tan(7pi/12)=(-1/2)/(1-sqrt(3)/2)
tan(7pi/12)=-1/(2(1-sqrt(3)/2)
tan(7pi/12)=-1/(2-sqrt(3))......rationalize
tan(7pi/12)=-(2+sqrt(3))/(((2-sqrt(3))(2+sqrt(3)))
tan(7pi/12)=-(2+sqrt(3))/(1)
tan(7pi/12)=-(2+sqrt(3))
tan(7pi/12)=-2-sqrt(3)

[QUOTE="MathLover1, post: 1099639, member: 280"] answer is [B]-2 - sqrt(3)[/B] tan(7pi/12)=sin(7pi/6)/(1+cos(7pi/6)) tan(7pi/12)=(-1/2)/(1-sqrt(3)/2) tan(7pi/12)=-1/(2(1-sqrt(3)/2) tan(7pi/12)=-1/(2-sqrt(3))......rationalize tan(7pi/12)=-(2+sqrt(3))/(((2-sqrt(3))(2+sqrt(3))) tan(7pi/12)=-(2+sqrt(3))/(1) tan(7pi/12)=-(2+sqrt(3)) tan(7pi/12)=[B]-2-sqrt(3)[/B] [/QUOTE]