Question

The expression cos(A-B) - cos(A+B) is equal to

1) -2sinAsinB
2) -2cosB
3) 2cosAcosB
4) 2sinAsinB

So far, all I've gotten is

cosxcosy + sinxsiny - cosxcosy - sinxsiny

I don't know where to go from there. I'm assuming that's zero, and I don't know which of the others equal 0... they all look the same.

Answer 1

well here's what u did wrong,
-cos(A+B)=-(cosAcosB-sinAsinB)=-cosAcosB+sinAsinB ... try reworking with this...

Answer 2

It's not -cos(A+B)... It's just subtracting +cos(A+B), isn't it? So that shouldn't change anything...

Answer 3

well u see, if you have a-(b-c), it is the same as a-(+b-c) but when u try to expand this, it becomes a-b+c, that's because two negatives will make a positive :)

Answer 4

Sooo... when you subtract cos(x + y), it turns into adding cos(x-y)....?

Answer 5

cos(A+B) will give you cosAcosB-sinAsinB , i agree to this, let's substitute this into the expression

cos(A-B) - \(cos(A+B)\)=cosAcosB+sinAsinB - \( (cosAcosB-sinAsinB) \)


cosAcosB+sinAsinB-cosAcosB+sinAsinB remember, two negatives make a positive
you'll have the cosAcosB-cosAcosB=0 and sinAsinB+sinAsinB=2sinAsinB

Answer 6

do u get it though?

Answer 7

Sorry, someone came over here :/

Answer 8

I think I get it, it's kind of weird though...

Answer 9

-(a-b) is not the same as -a-b, here's why, -(a-b) is the same as -1(a-b), if you try and use the distribution property, then you'll have (-1a)+(-1(-b)) which will become -a+b because -1(-b)=b two negatives make a positive...


so in a nut shell, -(-x)=x try and apply that :) it will make sense :)