Use the halfangle formulas to find the exact value of tan 5p

Use the half-angle formulas to find the exact value of tan 5pi/12

Solution

tan 5pi/12

Use the formula : tan(t/2)=+/-sqrt[(1-cos(t))/(1+cos(t))]
tan(5pi/12) = sqrt [ (1-cos(5pi/6) ) /(1+cos(5pi/6))

cos(5pi/6), we know that cos (pi/6) = 3/2
5pi/6 = pi-pi/6
cos(5pi/6) lies in quadrant II and is negative = -3/2

tan(5pi/12) = sqrt[(1- (-3/2)) / (1 + -3/2)]
= sqrt [(2+3)/(2-3)]