Hello,

The given eqn is,

cos x = l x l

If graph is drawn for y =x and y = cos x, then the graph will intersect at exactly one point ( 0.5 , 1 )

So, the number of real solutions for cos x = l x l is one.

The solution for above eqn will range from 0.5 to 1.

Let,

f(x)=x−cosx

Then:

f'(x)=1+sinx

By Newton Raphson's Method:

ai+1=ai − [ f(ai) / f'(ai) ]

By solving the above eqn by iterative method by using Newton Raphson's method, we find the approximate value of x = 0.739

So, the solution of given eqn is 0.739

Best Wishes.