Integrate the functions`sin^(-1)(cosx)`

Explanation

To solve the integral \(\int \sin^{-1}(\cos x) \, dx\), we will follow these steps:

### Step 1: Rewrite the cosine function
We know that \(\cos x = \sin\left(\frac{\pi}{2} - x\right)\). Therefore, we can rewrite the integral as:
\[ I = \int \sin^{-1}(\cos x) \, dx = \int \sin^{-1}\left(\sin\left(\frac{\pi}{2} - x\right)\right) \, dx \]

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