Let [t] denote the greatest integer less than or equal to t. If the function f(x)= {b^2 sin ((π)/2[(π)/2( cos x+ sin x) cos x]), x<0; (sin x-1/2 sin…

Let $\displaystyle [t]$ denote the greatest integer less than or equal to $\displaystyle t$. If the function $$f(x)=\left\{\begin{array}{cl} b^2 \sin \left(\frac{\pi}{2}\left[\frac{\pi}{2}(\cos x+\sin x) \cos x\right]\right), & x<0 \\ \frac{\sin x-\dfrac{1}{2} \sin 2 x}{x^3} & , x>0 \\ a & , x=0 \end{array}\right. $$ is continuous at $\displaystyle x=0$, then $\displaystyle a^2+b^2$ is equal to