Chapter 5 - Section 5.2 - Sum and Difference Formulas - 5.2 Problem Set - Page 288: 12

$= (2+\sqrt(3))$

$tan(75) = tan(120-45)$ $= \frac{[tan(120)-tan(45)]}{[1+tan(120)\times tan(45)]}$ $=\frac{[-\sqrt(3)-1]}{[1-\sqrt(3)*1]}$ Multiply numerator and denominator by $(1+\sqrt(3))$ to get $= [-(1-\sqrt(3))^2]/(1-3)$ $= (1+2\sqrt(3)+3)/2$ $= (4+2\sqrt(3))/2$ $= (2+\sqrt(3))$