Verify $\cos(x)=\frac{1-t^2}{1+t^2}$ with $t=\tan(\frac{x}{2})$ I was requested to verify, with $t=\tan(\frac{x}{2})$, the following identity:
$$\cos(x)=\frac{1-t^2}{1+t^2}$$
I'm quite rusty on my trigonometry, and hasn't been able to found the proof of this. I'm sure there may be some trigonometric property I should know to simplify the work. Could someone hint me or altotegher tell me how to solve this problem? I tried to simplify the RHS looking to get $\cos(x)$ out of it but failed.

Remember the high-school identities: $\;1+\tan ^2\theta=\frac1{\cos^2\theta}\;$ and $\;\cos2\theta=\cos^2\theta-\sin^2\theta$:
$$\frac{1-\tan^2\frac x 2}{1+\tan^2\frac x 2}=\cos^2\tfrac x2\bigl(1-\tan^2\tfrac x 2\bigr)=\cos^2\tfrac x2-\sin^2\tfrac x2=\cos x.$$
