The number of solutions of the equation sin^(-1)[x^2 + (1/3)] + cos^(-1)[x^2 - (2/3)] = x^2,

Question

The number of solutions of the equation

\(sin^{-1}\bigg[x^2 + \frac{1}{3}\bigg] + cos^{-1}\bigg[x^2 - \frac{2}{3}\bigg] = x^2,\)

for x ∈ [-1, 1], and [x] denotes the greatest integer less than or equal to x, is :

(1) 2

(2) 0

(3) 4

(4) Infinite

Answer 1

Given equation

So, form (1) and (2) we can conclude

So, number of solutions of the equation is zero.