Struggling with cos(a+b): My Frustration

[viet_jon]

Homework Statement

cos(a+b)

Homework Equations

find formulas for above

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.

 

[Dick]

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?

 

[praharmitra]

@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.

 

[Dick]

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.

 

[viet_jon]

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.

 

[Dick]

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.

 

[viet_jon]

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.

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...