Dear candidate,

As per the doubt raised by you,

cos (thetha) = adjacent/hypotenuse

If you consider the triangle while the proof is being done,

In right angled triangle QAO, angle(O)=90°

So, now in the QAO, AO=l, OQ = x

Now from Pythagoras theorem,

AQ = √(x^2+l^2)

So similarly when you will find the cos (A), you get l / √(x^2+l^2)

It's quite difficult to understand via this but try understanding the proof & apply the basics of trigonometry to get to know about the power of half for cos term.

Thanks.