Find the length of intercepts cuts on axes from the line `x sin alpha+y cos alpha=sin2alpha` and the co-ordinates of the mid-point of the line segment lies between the axes.

Explanation

`x sin alpha+-y cos alpha=sin2alpha`
`implies (x sin alpha)/(sin 2alpha)+(y cos alpha)/(sin 2alpha)=1`
`implies (x sin alpha)/(2 sin alpha cos alpha)+(y cos alpha)/( 2 sin alpha cos alpha)=1`
`implies (x)/(2cos alpha)+(y)/(2 sin alpha)=1`
Therefore, given line meets `X`-axis at point `A(2 cos alpha,0)` and `Y`- axis at point `B(0,2 sin alpha)`.
Length of intercept `AB`
`=sqrt((2cos alpha-0)^(2)+(0-2sinalpha)^(2))`
`=sqrt(4(cos^(2)alpha+sin^(2)alpha))`
`=2` units
Co-ordinates of mid-point of `AB`
`=((2cosalpha+0)/(2), (0+2sinalpha)/(2))`
`=(cosalpha,sinalpha)`