Statement I : The equation $\;(sin^{-1} x)^{3} + (cos^{-1} x)^{3} - a \pi^{3}=0\;$ has a solution for all $\;a \geq \large\frac{1}{32}\;$ .\[\] Statement II : For any $\;x \in R\;, sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}\;$ and $\; 0 \leq (sin^{-1}x - \large\frac{\pi}{4})^{2} \leq \large\frac{9 \pi^{2}}{16}\;$ .

Question

(a) Both statements I and II are true .\[\](b) Both statements I and II are false .\[\](c) Statements I is true and statement II is false .\[\](d) Statements I is false and statement II is true .