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Math Help - Proving Question(Factor Formulae)

  1. #1
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    Proving Question(Factor Formulae)

    Prove  <br />
(sinA+sinB)(sinA-sinB)=sin(A+B)sin(A-B)<br />
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  2. #2
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    Quote Originally Posted by Punch View Post
    Prove  <br />
(sinA+sinB)(sinA-sinB)=sin(A+B)sin(A-B)<br />
    Show us your work so far and we can help you where you get stuck.
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  3. #3
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    Using factor formulae, (sinA+sinB)(sinA-sinB)=2(sin(\frac{A+B}{2})cos(\frac{A-B}{2}))(2cos(\frac{A+B}{2})sin(\frac{A-B}{2}))

    stucked...
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  4. #4
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    Anyone care to tell me if I am on the right track and how to go on?
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  5. #5
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    Quote Originally Posted by Punch View Post
    Anyone care to tell me if I am on the right track and how to go on?
    Help required
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  6. #6
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    Hello, Punch!

    Prove: . (\sin A+\sin B)(\sin A-\sin B)\:=\:\sin(A+B)\sin(A-B)
    Start with the right side . . .

    \sin(A\;+\;B)\sin(A\;-\;B) \;=\;\bigg[\sin A\cos B\;+\;\cos A\sin B\bigg]\,\bigg[\sin A\cos B\;-\;\cos A\sin B\bigg]

    . - - . . . . . . . . . . . =\; \sin^2\!A\cos^2\!B \;\;-\;\; \cos^2\!A\sin^2\!B

    . . . . . . . . . . . = \; \sin^2\!A\overbrace{(1-\sin^2\!B)} - \overbrace{(1-\sin^2\!A)}\sin^2\!B

    . . . . . . . . . . =\; \sin^2\!A - \sin^2\!A\sin^2\!B - \sin^2\!B + \sin^2\!A\sin^2\!B

    . . . . . . . . . . . . . . . . . . = \;\sin^2\!A - \sin^2\!B

    . . . . . . . . . . . . . . = \;(\sin A + \sin B)\,(\sin A - \sin B)

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  7. #7
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    Quote Originally Posted by Soroban View Post
    Hello, Punch!

    Start with the right side . . .

    \sin(A\;+\;B)\sin(A\;-\;B) \;=\;\bigg[\sin A\cos B\;+\;\cos A\sin B\bigg]\,\bigg[\sin A\cos B\;-\;\cos A\sin B\bigg]

    . - - . . . . . . . . . . . =\; \sin^2\!A\cos^2\!B \;\;-\;\; \cos^2\!A\sin^2\!B

    . . . . . . . . . . . = \; \sin^2\!A\overbrace{(1-\sin^2\!B)} - \overbrace{(1-\sin^2\!A)}\sin^2\!B

    . . . . . . . . . . =\; \sin^2\!A - \sin^2\!A\sin^2\!B - \sin^2\!B + \sin^2\!A\sin^2\!B

    . . . . . . . . . . . . . . . . . . = \;\sin^2\!A - \sin^2\!B

    . . . . . . . . . . . . . . = \;(\sin A + \sin B)\,(\sin A - \sin B)
    Thanks! You are a great help! Can I solve it using factor formulae?

    How do I get as pro as you in trigonometry?
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  8. #8
    Super Member craig's Avatar
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    Quote Originally Posted by Punch View Post
    How do I get as pro as you in trigonometry?
    Want three words that will help you get to be a pro at mathematics?

    Practice practice practice.

    It's no good just reading a book on the subject, once you have done that get as many practice questions in as you can. It's the same with all topics in maths, some you might get straight way, others take a lot of work.

    Also don't worry about getting stuck, getting stuck is how you learn things Look through past examples see if they're any use to you, if not there's this wonderful forum filled with extremely intelligent people that you can post your questions on
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