# 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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