Q: Find $A = a + b$, where $\frac{a}{b}$ is the ratio of the area of the regions bounded by curve $y = \tan(x)$ and $\frac{4x^2}{\pi^2} + y^2 = 1$, a and b are coprimes.
I thought of assuming point $ (\frac{\pi\cos(x)}{2}, \sin(x))$ on the ellipse.
So, it also satisfies the first curve, so, $\sin(x) = \tan(\frac{\pi\cos(x)}{2})$
I am unable to proceed after this