The value of lim cos^(-1)(x - [x]^2) . sin^(-1)(x - [x]^2) x ∈ 0^(+) where [x] denotes the greatest integer

Question

The value of

\(\lim\limits_{x \to 0^{+}}\frac{cos^{-1}(x - [x]^2).sin^{-1}(x-[x]^2)}{x-x^3},\) where [x] denotes the greatest integer \(\leq\) x is :

(1) \(\pi\)

(2) 0

(3) \(\frac{\pi}{4}\)

(4) \(\frac{\pi}{2}\)

Answer 1

Correct answer is (4)