An algebra problem by Ankan Biswas

Problem would have a good meaning if domain of x was given

By using AM-GM inequality we can say that the minimum value of LHS for positive $a$ is $2$ for $a=1$ . On the other hand the maximum value of RHS is $2$ when $\cos x=1$ .

By these two facts we can say that $\textbf {both the sides are equal to 2}$ Hence $\huge a=1$