If `f(x)={asinpi/2(x+1), ,xlt=0(tanx-sinx)/(x^3),x >0` is continuous at `x=0` , then a equal (a)`1/2` (b) `1/3` (c) `1/4` (d) `1/6`

Explanation

To determine the value of \( a \) such that the function

\[
f(x) =
\begin{cases}
a \sin\left(\frac{\pi}{2} x\right) + 1 & \text{if } x < 0 \\
\frac{\tan x - \sin x}{x^3} & \text{if } x > 0
\end{cases}
...