Among the following functions defined on R into R, the constant function is

$\begin{array}{l}={\cos }^{2}x+{\cos }^2\left(x+\frac{\pi }{3}\right)+\sin x.\sin \left(x+\frac{\pi }{3}\right)\\ =1+\left({\cos }^2\left(x+\frac{\pi }{3}\right)-{\sin }^{2}x\right)+\frac{1}{2}\left(2\sin x.\sin \left(x+\frac{\pi }{3}\right)\right)\\ =1+\cos \left(x+\frac{\pi }{3}+x\right)\cos \left(x+\frac{\pi }{3}-x\right)+\frac{1}{2}\left(\cos \left(x+\frac{\pi }{3}-x\right)-\cos \left(x+\frac{\pi }{3}+x\right)\right)\\ =1+\frac{1}{2}\cos \left(2x+\frac{\pi }{3}\right)+\frac{1}{4}-\frac{1}{2}\cos \left(2x+\frac{\pi }{3}\right)\\ =\frac{5}{4}isacons\tan t\end{array}$