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    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.
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    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.
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    Isn't the formula:
     \cos A + \cos B = 2 \cos \left(\frac{A+B}{2} \right) \cos \left(\frac{A-B}{2} \right)

    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.
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    (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.
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    like you say, 2 cos A cos B = cos (A+B) + cos (A-B)

    so  2cos75cos15 = cos (75 + 15) + cos (75 - 15)

    so  cos75cos15 = \frac{( cos (75 + 15) + cos (75 - 15) )}{2}

     = \frac{cos 90 + cos 60}{2} = \frac {1/2}{2} = \frac{1}{4}

    you simply forgot about the "2" on the left
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    (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. :p:
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    (Original post by div curl F = 0)
    Isn't the formula:
     \cos A + \cos B = 2 \cos \left(\frac{A+B}{2} \right) \cos \left(\frac{A-B}{2} \right)
    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.
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    (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 :facepalm:
    • Thread Starter
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    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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