If $540^{\circ} < A < 630^{\circ}$ and $|\cos A|=\frac{5}{13}$, then $\tan \frac{A}{2} \tan A=$

If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$, then $\tan \left(\frac{\pi}{4}+\alpha\right)+4 \tan \left(\frac{\pi}{4}+\beta\right)=$

The general solution of the equation $\sin ^2 \theta+3 \cos ^2 \theta=$ $5 \sin \theta$ is

If $\cos ^{-1} 2 x+\cos ^{-1} 3 x=\frac{\pi}{3}$ and $4 x^2=\frac{a}{b}$, then $a+b$ is equal to