Prove that: `int_0^pix/(1+cosalphasinx)dx=(pialpha)/(sinalpha)`

Explanation

To prove that

\[ \int_0^\pi \frac{x}{1 + \cos \alpha \sin x} \, dx = \frac{\pi(\pi - \alpha)}{\sin \alpha} \]

we will start from the left-hand side and manipulate it step by step.

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