IF x cos(alpha)+ ysin(alpha)=1,

a b

xcos(Beta) + ysin(Beta)=1 and

a b

cos(alpha)cos(Beta) +

a²

sin(alpha)sin(Beta) =0 then

b²

prove that:

tan(alpha)tan(beta)={b²(x² - a²)}/{a²(y²- b²)}

Hi,

Square the equation one and two on both sides and ADD and simplify.
You will see taht the expression of third equation will come up i the addition which will be zero.

Then take x^2 terms on one side and y^2 terms on other side and sipmlify.
You will get the result.