# Thread: Need help with this cosine proof.

1. ## Need help with this cosine proof.

Hi there, I came across this cosine proof in my workbook but I'm having a very difficult time comprehending the proof statements.

Specifically, in the left column, second box I don't understand how b^2 = h^2 - 2cx - x^2 + c^2 was expanded from the Pythagorean Theorem in the box above it.

Moreover, how the heck does that get simplified and rearranged to b^2 = h^2 - x^2 - 2cx + c^2

I'm sure this is very simple math, but I just don't understand the rules for the operations. What is actually happening?

Beyond this, I just simply don't understand the logic to the rest of the proof. Why is there no pattern in finding out \Delta ADC when compared to how \Delta BDC is solved in the proof.

Previous to this proof, my only experience was working through a similar problem but with a Sine proof, it was much easier to comprehend and duplicate when I was faced with filling out a blank proof.

If anyone can help me I would REALLY appreciate it!

2. $\displaystyle b^2=h^2+(c-x)^2$

$\displaystyle b^2=h^2+(c-x)(c-x)$

$\displaystyle b^2=h^2+c(c-x)-x(c-x)$

$\displaystyle b^2=h^2+c^2-cx-cx+x^2$

$\displaystyle b^2=h^2+c^2-2cx+x^2$

As addition is commutative, the ordering of the terms doesn't matter, as long as they remain on the same side of the equation.