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Math Help - Proving Trigonometry function

  1. #1
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    Question Proving Trigonometry function



    How would we prove this? I am familiar with deriving trig but not this. Can someone please shed some light and show me step by step on how to do this? Thank you.
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    You can expand the RHS using compound angle formula.
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by florx View Post


    How would we prove this? I am familiar with deriving trig but not this. Can someone please shed some light and show me step by step on how to do this? Thank you.
    You should know that:

    cos(A+B) = cosA.cosB - sinA.sinB

    cos(A-B)= cosA.cosB + sinA.sinB

    Subtract these two equations.

    cos(A+B) - cos(A-B) = ????....(1)

    Now let u = A+B and v= A-B

    substitute this into equation (1)
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    Thank you for your help.

    After I plugged that into the equation again the (cos a+b * cos a-b) cancels out and we are left with (-sin a + b sin a - b) - (sin a + b sin a - b) which should equal to -2 sin a + b sin a - b.

    Now what would we do next? And what about the 2 in the denominator of the right hand side of the equation?
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  5. #5
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by florx View Post
    Thank you for your help.

    After I plugged that into the equation again the (cos a+b * cos a-b) cancels out and we are left with (-sin a + b sin a - b) - (sin a + b sin a - b) which should equal to -2 sin a + b sin a - b.

    Now what would we do next? And what about the 2 in the denominator of the right hand side of the equation?
    okay.

    So you have:

    cos(A+B) - cos(A-B) = -2 sinA.sinB .....(1)

    As I said above:

    let u = A+B and let v = A-B......(2)

    Clearly, the left side of the equation them becomes: cosu - cosv

    your right side has  -2 sinA.sinB

    Convert u and v from (2) in terms of A and B
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