# Homework Help: Solve Cos(a+b)

1. Sep 14, 2008

### viet_jon

1. The problem statement, all variables and given/known data

cos(a+b)

2. Relevant equations

find formulas for above

3. The attempt at a solution

cos (a+b)

= cos (a-(b))

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

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

I been scratching my head at this for hours now, and I still can't figure out how this works.

2. Sep 14, 2008

### Dick

Re: cos(a+b)

cos(a+b) is not equal cos(a-b). Do you have a formula for one that you are trying to transform into a formula for the other?

3. Sep 14, 2008

### praharmitra

Re: cos(a+b)

@dick - no, he has written a - b, but i think he meant a - (-b), as he has followed it up with the relevant calculations.

What i can't understand is what the question is. You seem to have solved and found solution already.

4. Sep 14, 2008

### Dick

Re: cos(a+b)

I agree, my question was trying to get at what the question is. I'm guessing it's given cos(a+b) find cos(a-b). And it is done, except for general sloppiness in the whole statement and stating the parts that make it work like cos(-b)=cos(b) and sin(-b)=-sin(b). I was just running around looking for unanswered questions.

5. Sep 15, 2008

### viet_jon

Re: cos(a+b)

opps, sorry guys..... typo

cos(a+b)= cos (a-(-b))

=cosAcos(-b) + sin(a)sin(-b)

=cosAcosB - sinAsinB

I don't understand how the second line comes in. Where does sin come from?

The question asks to find formulas for cos(a+b). The answer is copied right out of my prof's notes, I just don't understand how it works.

6. Sep 15, 2008

### Dick

Re: cos(a+b)

You're professor must have ALREADY derived cos(a-b)=cos(a)cos(b)+sin(a)sin(b). You now want a formula for cos(a+b) without repeating something like the previous derivation. If you write a+b=a-(-b) then you've written the sum as a difference and you can use the difference formula you've already derived.

7. Sep 15, 2008

### viet_jon

Re: cos(a+b)

thnkx, I see what the notes mean now. Yes, cos(a-b) was derived on a page earlier.....

so we set cos(a+b) = cos(a-(-b)) so it fits the cos(a-b) derivation, so we don't have to do it all over again.

got it!! thnkx...