# How do you prove that tan(-x) = -tanx

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`tan(-x)=-tanx`

To prove, express the left side with its equivalent positive angle.

`tan(2pi-x)=-tanx`

Then, apply the identity of difference of two angles for tangent.

`(tan 2pi-tanx)/(1+tan2pitanx)=-tanx`

Since `tan 2pi=0` , left side simplifies to :

`(-tanx)/1=-tanx`

`-tanx =- tanx`

**Since the left side simplifies to -tanx and this proves that tan(-x) is equal to -tanx.**