Jika cos x 4/5 maka tan x/2 sama dengan

cos x = 4/5
sin x = √(1 - cos² x) = 3/5

tan x = sin x/cos x = 3/4

tan x = tan 2(x/2)
tan 2(x/2) = 3/4
2 tan (x/2) / (1 - tan² (x/2)) = 3/4
Kali silang
8 tan (x/2) = 3 - 3 tan² (x/2)
3 tan² (x/2) + 8 tan (x/2) - 3 = 0
(3 tan (x/2) - 1)(tan (x/3) + 3) = 0

3 tan (x/2) - 1 = 0 ---> tan (x/2) = 1/3 ✔
atau
tan (x/2) + 3 = 0 ---> tan (x/2) = -3 ✔