if the tangent of the angle between the lines of regression of Y on X and X on Y is 0.6, and the S.D. of Y is twice that of X, find the correlation coefficient between X and Y.

Let $L_{yx}\ $be the line of regression of y on x.

Let the angle made by $L_{yz}\ $with X-axis be $\mathrm{\theta}$

$\mathrm{\therefore }$ Tangent of the angle made by $L_{yz}$ with X- axis = tan $\mathrm{\theta}$ = 0.6

But , slope of any line with X-axis = tan $\mathrm{\theta}$

However, …