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    Hello,
    Does anyone know how to prove that

     cos(\frac{pi}{3} - theta ) -  sin(\frac{pi}{6} - theta ) = cos(theta) ?

    I'm getting extremely confused!!

    (Also obviously having trouble using symbols!)
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    That's not true. Maybe it should read:

    \cos(\frac{\pi}{3} - \theta) + \sin(\frac{\pi}{6}-\theta) = \cos(\theta)

    Do you know the formulae for \sin(A \pm B) and \cos(A \pm B)?
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    apologies, that is what it is suppposed to read. no, i dont think i do. or, i did know and i have now forgotten? either are very possible!!
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    (Original post by kate__88)
    apologies, that is what it is suppposed to read. no, i dont think i do. or, i did know and i have now forgotten? either are very possible!!
    Well I'll tell you the identities you can use. See if you can do it now.

    \sin(A - B) = \sin(A)cos(B) - \cos(A)\sin(B)

    \cos(A - B) = \cos(A)cos(B) + \sin(A)\sin(B)
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    i'm thinking that the second identity fits this equation better. but there are differing values for A and b...
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    or do you use both??
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    Yeah use both.
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    haha oh dear still not getting anywhere. which values do you use for a and b? are the values you use different for the two different equations. i'm never any good at proving things!!
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    I'm gonna let theta = x here

    cos(pi/3 -x) + sin(pi/6 - x)

    Using cos(A-B) = cos(A)cos(B) + sin(A)sin(B)
    cos(pi/3 - x) = cos(pi/3)cos(x) + sin(pi/3)sin(x) (here A = pi/3 and B =x)

    Using sin(A-B) = sin(A)cos(B) - sin(B)cos(A)
    sin(pi/6 - x) = sin(pi/6)cos(x) - sin(x)cos(pi/6)

    Therefore:

    cos(pi/3 -x) + sin(pi/6 - x)
    = cos(pi/3)cos(x) + sin(pi/3)sin(x) + sin(pi/6)cos(x) - sin(x)cos(pi/6)

    Try it from there?

    You have to realise that equations like sin(A-B) = sin(A)cos(B) - sin(B)cos(A) are actually identities - they're true for all values of A and B. It's not like simultaneous equations that you need to have two equations with the same A and B.
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    i got to the two separate equations before (with the help of the suggestion of the identities) by assuming that A and B would be different. i did the same steps, but i was unable to merge the equations. i understand how you have merged the two equations but unfortunately i'm still struggling to come to the final line where cos theta will equal that equation??? any other hints please? (without of course completely giving me the answer! )
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    Notice how cos(pi/3) is a number. Maybe it will help to actually write down what cos(pi/3), sin(pi/6) etc actually are?
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    yaya!! i got it! thanks so much for all your help!!
 
 
 
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