Question

Prove that $\tan (180-x)=-\tan \left(x\right)$

Answer 1

We know the identity

$\tan (A-B)=\frac{\tan A–\tan B}{1+\tan A\times \tan B}$

Now we will substitute$\mathrm{A}=180$ and $B=x$ in the above identity we get

$\tan (180-x)=\frac{\tan 180–\tan x}{1+(\tan 180)\times (\tan x)}$

We have learnt that $\tan 180=0$

so we get the above equation as

$\tan (180-x)=\frac{0–\tan x}{1+0\times \tan x}$

$\tan (180-x)=-\tan \left(x\right)$

Hence Proved