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

To find the length of the intercepts cut on the axes from the line \( x \sin \alpha + y \cos \alpha = \sin 2\alpha \) and the coordinates of the midpoint of the line segment that lies between the axes, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the equation in intercept form**:
The general form of a line with intercepts on the axes is given by:
\[
\frac{x}{a} + \frac{y}{b} = 1
...