$\begin{array}{l} B = {\cos ^2}x + {\cos ^2}\left( {x - \dfrac{\pi }{3}} \right) + {\cos ^2}\left( {x + \dfrac{\pi }{3}} \right)\\ B = \dfrac{{1 + \cos 2x}}{2} + \dfrac{{1 + \cos \left( {2x - \dfrac{{2\pi }}{3}} \right)}}{2} + \dfrac{{1 + \cos \left( {2x + \dfrac{{2\pi }}{3}} \right)}}{2}\\ B = \dfrac{{3 + \cos 2x + \left[ {\cos \left( {2x - \dfrac{{2\pi }}{3}} \right) + \cos \left( {2x + \dfrac{{2\pi }}{3}} \right)} \right]}}{2}\\ B = \dfrac{{3 + \cos 2x + 2\cos 2x\cos \dfrac{{2\pi }}{3}}}{2}\\ B = \dfrac{{3 + \cos 2x + 2\cos 2x\cos \left( {\pi - \dfrac{\pi }{3}} \right)}}{2}\\ B = \dfrac{{3 + \cos 2x - 2\cos 2x\cos \dfrac{\pi }{3}}}{2}\\ B = \dfrac{{3 + \cos 2x - \cos 2x}}{2} = \dfrac{3}{2} \end{array}$
