Circular Trigonometry Question

Question

Find tan 75° exactly using an angle addition or subtraction formula.

Find the exact value of tan 75°

Which answer is it

A: 3+√3 / 3-√3

B: √3 + √2 / 8

C: 2+√6 / 2-√6

D: √3 - 1 / 8

Answer 1

tan75 = tan(45+30) = (tan45 + tan30)/(1=tan45tan30) = (1+1/sqr3)/(1=1/sqr3) = 2+sqr3 = about 3.732

use the addition formula for tangents

tan(A+B) = (tanA + tanB)/(1=tanAtanB) with A = 45 and B= 30