Question 425935
this looks like it's straight algebra manipulation.


let a = cot(alpha)
let b = cot(beta)
let t = cot(theta)


t is equal to the lower case T, no to be confused with + which is the plus sign.


you start with m*(a-t) = n*(b+t)


multiply out each factor to get:


m*a - m*t = n*b + n*t


add m*t to  both sides of the equation and subtract n*b from both sides of the equation to get:


m*a - n*b = m*t + n*t


factor to get:


m*a - n*b = (m+n)*t


commute to get:


(m+n)*t = m*a - n*b


substitute for t,a,b to get:


(m+n) * cot (theta) = m*cot(alpha) - n*cot(beta)