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.

$$\cos(x)=\cos^2(x/2)-\sin^2(x/2)=(1-t^2)/(\sec^2(x/2))=(1-t^2)/(1+t^2)$$
