If 3cos2x=3−1cosx+1, the number of solutions of the given equation whenx∈0,π2  is

The given equation is 3cos2x=(3-1)cosx+1 This can be simplified as below 3cosxcosx−1+cosx−1=03cosx+1cosx−1=0,x∈0,π2It gives x=0 is only solution for the above equation in the given interval, hence the number of solutions is 1.