Question

How do you verify `tan (pi - x) = -tanx`?

Answer 1

Verify trig expression

Explanation:

Two ways.
1. First way. Using the trig unit circle.
tan (pi - x) = - tan x
2. Second way. Apply the identity:
`tan (a - b) = (tan a - tan b)/(1 - tan a.tan b)`
`tan (pi - x) = (tan pi - tan x)/(1 - tan (pi).tan x)`

Since tan (pi) = 0, therefor:
`tan (pi - x) = - tan x`