If $z_1=5-2 i$ and $z_2=3+i$, where $i=\sqrt{-1}$, then $\arg \left(\frac{z_1+z_2}{z_1-z_2}\right)$ is

The co-ordinates of the foot of the perpendicular from the point $(0,2,3)$ on the line $\frac{x+3}{5}=\frac{y+1}{2}=\frac{z+4}{3}$ is

The slope of tangent at $(x, y)$ to a curve passing through $\left(1, \frac{\pi}{4}\right)$ is $\frac{y}{x}-\cos ^2 \frac{y}{x}$, then the equation of curve is

If $\cos ^{-1}\left(\frac{12}{13}\right)+\sin ^{-1}\left(\frac{3}{5}\right)=\sin ^{-1} \mathrm{P}$, then the value of $P$ is