How do you prove (tan x)(cos x)=sin x?

See Below.

Explanation:

L.H.S. = $\left(\tan x\right) \left(\cos x\right)$

= $\left(\sin \frac{x}{\cancel{\cos x}}\right) \left(\cancel{\cos x}\right)$

= $\sin x$ = R.H.S

[As we know that $\tan \theta = \left(\text{perpendicular")/("base") = ("perpendicular"/"hypotenuse")/("base"/"hypotenuse}\right) = \sin \frac{\theta}{\cos} \theta$]

Hope it helps.