Question

How do you prove `tan (2x)/tan x=2`?

Answer 1

Prove `tan 2x/(tan x) = 2`

Ans: Wrong equation.

Explanation:

This trig equation is wrong.
Example: `x = pi/4` --> tan x = 1 --> `tan 2x = tan (pi/2) =` infinity.
Another proof by using trig identity.
`tan 2x = (2tan x)/(1 - tan^2 x)`

`(tan 2x)/(tan x) = 2/(1 -tan^2 x)`
So, the expression omits the quantity: `(1 - tan^2 x)`