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Question 425935: hi am stuck on the cotangent formula for triangles
how do we get from number 1 to number 2
1. m{cot α-cotθ} = n{cot β + cot θ}
2. (m+n) cot θ = m cot α - n cot β
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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)
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