#2015_29 Continuity at a point

Calculus Level 3

f(x)={1sin3(x)3cos2(x)for x<π2afor x=π2b(1sin(x))(π2x)2for x>π2\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 aa and bb such that the function f(x)f(x) above is continuous at x=π2x=\dfrac { \pi }{ 2 } .

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