Half-Angle Formulas...3

[nycmathguy]

Section 5.5

 

[MathLover1]

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)

 

[nycmathguy]

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)

Another sign error. Cool. Take away a few points.