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    how do we use the factor formulae when we have coefficients to the sin values ( amd cos)

    sinA - SinB = 2cos (A+B / 2) sin A-B / 2

    if it has coefficients such as
    5sin (A-30) - 4sin (A+30) where do we place the 5 and 4 in the expansion???

    or does it mean i have to expand each addition formulae seperatly?
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    Chittesh14
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    (Original post by pondsteps)
    how do we use the factor formulae when we have coefficients to the sin values ( amd cos)

    sinA - SinB = 2cos (A+B / 2) sin A-B / 2

    if it has coefficients such as
    5sin (A-30) - 4sin (A+30) where do we place the 5 and 4 in the expansion???

    or does it mean i have to expand each addition formulae seperatly?
    You could split the first term up (let's call it x.. the second one y)

    To turn 5x - 4y into x + (4x - 4y) = ....
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    (Original post by pondsteps)
    Chittesh14
    Sorry I forgot to reply to this -_- and remember today.
    I'm outside right now, I'll reply to this in detail once I come back home - sorry for the wait !

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    (Original post by pondsteps)
    how do we use the factor formulae when we have coefficients to the sin values ( amd cos)

    sinA - SinB = 2cos (A+B / 2) sin A-B / 2

    if it has coefficients such as
    5sin (A-30) - 4sin (A+30) where do we place the 5 and 4 in the expansion???

    or does it mean i have to expand each addition formulae seperatly?
    It really depends on what the question is asking lol. What is the question and what is the answer?
    You could expandd each addition formulae separately and come up with two terms again but nothing cancels out realy due to the 5 and 4 - the coefficients are not the same.
    Hence why, it would be more appropriate as SeanFM said to split the terms up into x and y and rewrite it as x + 4x - 4y to make sure the coefficient is the same.

    In case you don't understand, x is sin(A-30) and y is sin(A+30).
    5sin (A-30) - 4sin (A+30)= 5x - 4y = x + 4x - 4y.... Use the sin A + sin B for 4x + 4y where 4(x+y) so 4(sin(A-30) + sin(A+30)) = 4(x+y) = 4x + 4y.
    Then, you can add x which is sin(A-30) to 4x + 4y, this time you'll see you need to expand the identity using addition formulae and eventually you'll come to an answer.
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    If you use that method and simplify you can get two terms in sin and cos only and then you can even write it using harmonic identities.
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    thank you!!
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    (Original post by pondsteps)
    thank you!!
    No problem


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