The number of solutions of `sin(x/2) + 2 pi x = x^2 + pi^2 + 1` must be

Explanation

[1]
`therefore sin(x/2 - 1 = x^2 - 2 pi r + pi^2 implies sin(x/2) - 1 = (x - pi)^2`
`LHS le 0` and `RHS ge 0`
then solution is obtained is LHS = RHS = 0 and `X = pi` satisfies both
Hence, number of solutions is one.