Half angle/double angle formula

Question

negative radical 4root3 +7 .How do you solve the rest of this? Its supposed to be -2-root 3

Answer 1

The double angle and half angle formulas don't work here. tan(a+b) is a better fit.

tan(105) = tan(60 + 45) = (tan(60) + tan(45))/(1-tan(60)tan(45)) = (√3 + 1)/(1-√3(1)) = - √(√3 + 1)/(√3-1)

Now you need to multiply the numerator and denominator by the denominator's conjugate, √3 +1, to remove the radical from the denominator.

-(√3 + 1)²/((√3 -1)(√3+1) =(-4 -2√3)/(3-1) = -2 - √3