Tricky Calculus Question II

Calculus Level 4

\[\large \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{k}{1+\cos(a)\sin(x)}dx= \frac{\pi }{\sin(a)}\]

The equation above holds true for constants \(a\) and \(k\). Find \(k\).

Note: Consider \(0 < a < \tfrac12\pi\).

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