Let `f(x)=e^(cos^(-1){sin(x+pi/3)})` Then, `f((8pi)/9)=` (a)`e^(5pi//18)` (b) `e^(13pi//18)` (c) `e^(-2pi//18)` (d) none of these

Explanation

To solve the problem \( f(x) = e^{\cos^{-1}(\sin(x + \frac{\pi}{3}))} \) and find \( f\left(\frac{8\pi}{9}\right) \), we will follow these steps:

### Step 1: Substitute \( x \) in the function
We start by substituting \( x = \frac{8\pi}{9} \) into the function:
\[ f\left(\frac{8\pi}{9}\right) = e^{\cos^{-1}\left(\sin\left(\frac{8\pi}{9} + \frac{\pi}{3}\right)\right)} \]

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