Thread: Law of Tangents

Hey MHF, today in class we took Melloweid's formula, then the teacher gave us this equation and only two students were able to solve it
I'm 100% sure I'm going to have to use Melloweid's formula to derive it.

Law of Tangents For any triangle, derive the Law of Tangents.


Any ideas?
Thanks

Hi the Melloweird's formula are given there

Mollweide's formula - Wikipedia, the free encyclopedia

if you take the second one and divide it by the firt one you end up with


we know that

so


The tricky part is the find out Why in the world


But this is the funny part so I leave it to you!

Lol, I will give it a thought and see how it goes, if I find it I will post the results. If not, then know that I have failed

I'm gonna call it a night

dang I think I made a mistake there! Hold on i'll change few thing..

there it should be fine. Sorry about that.

Haha no way, I couldn't.. I give up :/

Here is how you solve it

sin(a-b) = sin a*cos b - sin b*cos a

Let a = pi/2 and b = x = (A+B)/2

sin ( /2 - x) = sin /2*cos x - sin x* cos /2

since sin pi/2 = 1 and cos pi/2 = 0

sin ( pi/2 - x) = 1*cos x - sin x*0

sin ( pi/2 - x) = cos x

note: I personaly just write down my trigo circle and see it eazier from there.

Have a good day