यहाँ $\cos \theta  = \frac{3}{5}$ व $\cos \phi = \frac{4}{5}$.

इसलिए  $\cos (\theta  – \phi ) = \cos \theta \cos \phi + \sin \theta \sin \phi $

$ = \frac{3}{5}.\frac{4}{5} + \frac{4}{5}.\frac{3}{5} = \frac{{24}}{{25}}$

लेकिन $2{\cos ^2}\left( {\frac{{\theta  – \phi }}{2}} \right) $

$= 1 + \cos (\theta  – \phi ) = 1 + \frac{{24}}{{25}} = \frac{{49}}{{50}}$

$\therefore$ ${\cos ^2}\left( {\frac{{\theta  – \phi }}{2}} \right) = \frac{{49}}{{50}}$. 

अत: $\cos \left( {\frac{{\theta  – \phi }}{2}} \right) = \frac{7}{{5\sqrt 2 }}$.