Use an addition or subtraction formula to find the exact val

Use an addition or subtraction formula to find the exact value of tan 75 degree = squareroot A + 1/squareroot B - 1 A = B =

Solution

tan 75= tan(45+30)

and tan(A+B)= (tan A + tan B)/(1-tanAtanB)

tan(45+30)= (tan45+tan30)/(1-tan45tan30)

tan75 = (1 + 1/sqrt3)/(1-1(1/sqrt3))

                 = (sqrt3 + 1)/(sqrt3 -1)