Question

From given: $p+q=2\cot \theta$ and $p-q=2\cos \theta$. Also $pq=(\cot \theta +\cos \theta )(\cot \theta -\cos \theta )={\cot }^2\theta -{\cos }^2\theta$. $p^2-q^2=(p+q)(p-q)=2\cot \theta \times 2\cos \theta =4\cot \theta \cos \theta$. We need to show this equals $4\sqrt{pq}$. Squaring both sides and verifying the identity.