# What is tan(x-pi)?

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We'll have to use the following identity to compute tan(x - `pi` ).

`tan (a - b)` = `(tan a - tan b)/(1 + tan a*tan b)`

We'll replace a and b by x and `pi`, such as:

`tan (x - pi )` = `(tan x - tan pi)/(1 + tan x*tan pi)`

But `tan pi = sin pi/cos pi = 0/-1 = 0`

`tan (x - pi) = (tan x - 0)/(1 + tan x*0)`

`tan(x - pi) = tan x`

**Therefore, the value of tangent of the difference `x - pi` remains the same as the value of the tangent of the angle x.**

tan(x-pi) = (tanx - tan pi)/(1-tanx.tan pi)

we know that tan pi = 0

= (tanx - 0)/(1- tanx*0)

= tanx/1

= tan x