Question

Can someone help me to prove this?
(cosA+cosB)/(cosA-cosB)=cot((1/2)(A-B))cot((1/2)(A+B))

Answer 1

we can use a few identities to rewrite the right hand side. First right it as product of two cosines over product of two sines. Then I used

cos(u +/- v)= cos(u)cos(v) -/+ sin(u)sin(v)

sin(u +/- v)= sin(u)cos(v) +/- cos(u)sin(v)

sin^2(x)=(1-cos(2x))/2
cos^2(x)=(1+cos(2x))/2.

its just a matter of running the algebra then. Let me know if you need help with any steps or getting started.

Answer 2

write*

Answer 3

yeah I need help. Im really confused with this

Answer 4

Please can you show me the work?

Answer 5

Trying to learn trigonometry

Answer 6

ok the right hand side can be written...

{cos((A-B)/2)*cos((A+B)/2)}/{sin((A-B)/2)*sin((A+B)/2)}

Answer 7

each term is in the form of the first 2 identities that i posted

Answer 8

so if you write them out and then multiply you'll get terms in the form of the 3rd and 4th identities I posted

Answer 9

It all simplifies down to the left hand side

Answer 10

let me check it out. I will write you if i get lost. Thanks

Answer 11

Yep let me know.

Answer 12

http://www.sosmath.com/trig/Trig5/trig5/trig5.html here are a bunch of identities

Answer 13

These trig problems are always mindless manipulation of symbols. I'll have a go at it and get back to you shortly.

Answer 14

got it!

Answer 15

good :)

Answer 16

OK. The sum and difference formulae for cosines are as follows:

CosA + CosB = 2cos((A+B)/2)cos((A-B)/2) and

CosA - CosB = -2sin((A+B)/2)sin((a-B)/2)

So, your LHS = -cot((A+B)/2)cot((A-B)/2)

Note. I have a minus sign in front of your solution.

Answer 17

i had a negative as well

Answer 18

yeah the solution has a - sign

Answer 19

emun i answered one of your old physics questions, when you were asking about dimensions you meant units right?

Answer 20

yeah. I dint know how to put that question into english. And your right, i ment units.

Answer 21

ok, I've heard units called dimensions before I was just making sure that's what you meant.

Answer 22

In spanish we say dimension. I supposed it was the same in English. lol