Find the values of a and b if f is continuous at x=0, where
`f(x)={:{((sinx + cos x)^(cosec x), , - pi/2 lt xlt 0),( a, , x=0 ), ((e^(1//x)+e(2//x)+e^(3//x))/(ae^(-2+1//x ) + be^(-1+3//x)),, 0 lt x lt pi/2):}`

Explanation

To find the values of \( a \) and \( b \) such that the function \( f(x) \) is continuous at \( x = 0 \), we need to ensure that the limit of \( f(x) \) as \( x \) approaches 0 from the left equals \( f(0) \), and that this equals the limit of \( f(x) \) as \( x \) approaches 0 from the right.

### Step 1: Define the function and find \( f(0) \)
Given:
\[
f(x) =
\begin{cases}
(\sin x + \cos x)^{\csc x} & \text{for } -\frac{\pi}{2} < x < 0 \\
...