Question

Let $C_1:y=4x;C_2:y=\sin x\text{and}{C}_3:y=f\left(x\right)$ be the three curves passing through origin 'O' and defined in $[0,\frac{\pi }{2})$. From a point P on $C_2$ lines parallel to x-axis and y-axis meet $C_1\text{and}{C}_3$ at Q and R respectively as shown such that areas of curved regions OPQ and OPR are equal for all positions of point P. If $f\left(\frac{\pi }{4}\right)=\frac{1}{\sqrt{2}}+\frac{1}{a}-\frac{\pi }{b\sqrt{2}};$ (where a and b are integers) then (a + b) equal to

Answer 1

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