#2015_29 Continuity at a point

Calculus Level 3

\[\large{ f(x) = \begin{cases} \dfrac{1-\sin^3(x)}{3\cos^2(x)} & \text{for } x<\dfrac\pi2 \\ a & \text{for } x=\dfrac\pi2 \\ \dfrac{b(1-\sin(x))}{(\pi-2x)^2} & \text{for } x>\dfrac\pi2\\ \end{cases}} \]

Find the sum of values of \(a\) and \(b\) such that the function \(f(x)\) above is continuous at \(x=\dfrac { \pi }{ 2 } \).

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