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Math Help - Help me to prove this! My brainjuice is OVERHEATING!!!

  1. #1
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    Question Help me to prove this! My brainjuice is OVERHEATING!!!

    Help me please~ Anyone?

    Question:
    Prove this identity.
    1+cos2A-cos2B-cos2(A+B)=4sin(A+B)cosAcosB

    HELP! I only able to proceed 1 step only, and then, it just go back to the question again when i further solving it! Dying...
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  2. #2
    MHF Contributor red_dog's Avatar
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    1+\cos 2A-\cos 2B-\cos 2(A+B)=2\cos^2A-2\cos\frac{2B+2(A+B)}{2}\cos\frac{2B-2(A+B)}{2}=

    =2\cos^2A-2\cos(A+2B)\cos A=2\cos A(\cos A-\cos(A+2B))=

    =2\cos A\cdot 2\sin\frac{A+2B-A}{2}\sin\frac{A+2B+A}{2}=

    =4\cos A\sin B\sin(A+B)
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  3. #3
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    Mar 2009
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    Thanks RedDog!
    But is there any missing?

    How it transform from
    1+\cos2A-\cos2B-\cos2(A+B)
    to this
    =2\cos^2A-2\cos(A+2B)\cos A
    ?
    (Perhaps can help me with explaining each other steps too?)

    Sorry my trigo just way too sux. Help you can teach me, please~
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