The number of real solutions of the equation sin−1(∞∑i=1xi+1−x∞∑i=1(x2)i)=π2−cos−1(∞∑i=1(−x2)i−∞∑i=1(−x)i) lying in the interval (−12,12) is . (Here, the inverse trigonometric functions sin−1x and cos−1x assume values in [−π2,π2] and [0,π], respectively.)

The number of real solutions of the equation sin−1(∞∑i=1xi+1−x

1.	The number of real solutions of the equation sin−1(∞∑i=1xi+1−x∞∑i=1(x2)i)=π2−cos−1(∞∑i=1(−x2)i−∞∑i=1(−x)i) lying in the interval (−12,12) is . (Here, the inverse trigonometric functions sin−1x and cos−1x assume values in [−π2,π2] and [0,π], respectively.)
Answer» The number of real solutions of the equation ${sin}^{- 1} (\infty \sum i = 1 x^{i + 1} - x \infty \sum i = 1 {(\frac{x}{2})}^{i}) = \frac{π}{2} - {cos}^{- 1} (\infty \sum i = 1 {(- \frac{x}{2})}^{i} - \infty \sum i = 1 (- x)^{i})$ lying in the interval $(- \frac{1}{2}, \frac{1}{2})$ is . (Here, the inverse trigonometric functions ${sin}^{- 1} x$ and ${cos}^{- 1} x$ assume values in $[- \frac{π}{2}, \frac{π}{2}]$ and $[0, π]$ , respectively.)