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Product to Sum Formulae watch

1. Hi all,

I've been doing an exercise using the product to sum formulae
E.G. 2 cos A cos B = cos (A+B) + cos (A-B) and the others... its been fine upto now, but now I've got to a set of questions and they have completely stumped me.

One example is cos 75 cos 15. (Which = 1/4)
I tried to do this the regular way, which was unsuccessful giving cos 90+cos 60 = 1/2.
Then I made cos 75 into 2 cos 37.5, but that didnt work either.

I've completely ran out of ideas, can anyone help me with this question?

Thanks.
2. I'm not entirely sure what you're trying to do with cos75cos15, but note that 75 = 45 + 30 and 15 = 45 - 30.

Also, you know that 2cos75cos15 = cos90 + cos60, so cos75cos15 is half that, i.e. 0.5(cos90 + cos60) = 0.25.
3. Isn't the formula:

Now use: A+B = 150 and A-B = 30 and this should work correctly since cos 60 = 0.5 and theres an extra 0.5 in the formula.
4. (Original post by Bowlestown)
Hi all,

I've been doing an exercise using the product to sum formulae
E.G. 2 cos A cos B = cos (A+B) + cos (A-B) and the others... its been fine upto now, but now I've got to a set of questions and they have completely stumped me.

One example is cos 75 cos 15. (Which = 1/4)
I tried to do this the regular way, which was unsuccessful giving 1/2[cos 90+cos 60] = 1/4.Then I made cos 75 into 2 cos 37.5, but that didnt work either.

I've completely ran out of ideas, can anyone help me with this question?

Thanks.
fixed
5. like you say,

so

so

you simply forgot about the "2" on the left
6. (Original post by Bowlestown)
Hi all,

I've been doing an exercise using the product to sum formulae
E.G. 2 cos A cos B = cos (A+B) + cos (A-B) and the others... its been fine upto now, but now I've got to a set of questions and they have completely stumped me.

One example is cos 75 cos 15. (Which = 1/4)
I tried to do this the regular way, which was unsuccessful giving cos 90+cos 60 = 1/2.
You didn't divide by 2.

2 cos 75 cos 15 = cos 90 + cos 60 = 1/2.

Edit: The latest thing. How many ways can we tell someone to divide by 2.
7. (Original post by div curl F = 0)
Isn't the formula:
Those two formulae are equivalent, except different definitions of A and B. i.e. let P = A + B and Q = A - B in his formula, then your formula comes out in terms of P and Q.
8. (Original post by Swayum)
Those two formulae are equivalent, except different definitions of A and B. i.e. let P = A + B and Q = A - B in his formula, then your formula comes out in terms of P and Q.
Right you are and it looks more useful in the form given by the OP but being set in my ways I always use it the less useful way
9. Thanks all, as you can see I make small little errors haha. Ah well, i'm not very good at maths but keep trying! Thanks guys, will +ve rep.

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