If 3 tan (x - 15o) = tan (x + 15o), 0 ≤ x ≤ 90o, find x.
Let tan (15°) = tan(45°-30°)
We know that
We now
And
So, 3 tan (x - 15o) = tan (x + 15o) can be written as follows
(3 tan x – 3tan15)(1-tan x × tan15) = (1+tan x × tan15)(tan x + tan15)
3 tan x – 3 tan15-3 tan2x tan(15-3) tan x tan215 = tan x + tan15 + tan2x tan15 + tan x tan215
Solving the equation,
And putting
We get tan x - 1 = 0
Therefore, tan x =1
So, x=45°
Or