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Math Help - [SOLVED] Verify that the equation is an identity.

  1. #1
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    [SOLVED] Verify that the equation is an identity.

    Sin 4\alpha = 4 Sin\alpha Cos\alpha Cos 2\alpha
    Last edited by something3k; October 7th 2008 at 06:30 PM. Reason: it was kind of messy
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by something3k View Post
    Sin 4\alpha = 4 Sin\alpha Cos\alpha Cos 2\alpha
    start on the left hand side and use the double angle formula for sine: \sin 2 \alpha = 2 \sin \alpha \cos \alpha

    note that \sin4 \alpha = \sin [2(2 \alpha)]
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  3. #3
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    so would that equal 4 \sin\alpha \cos\alpha?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by something3k View Post
    so would that equal 4 \sin\alpha \cos\alpha?
    no, follow the rule: sin(2A) = 2*sinA*cosA
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  5. #5
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    Hello, something3k!

    Identity: . 2\!\cdot\!\sin\theta\!\cdot\!\cos\theta \:=\:\sin2\theta


    \sin4\alpha \:= \:4\!\cdot\!\sin\alpha\!\cdot\!\cos\alpha\!\cdot\!  \cos2\alpha
    Or start on the right side . . .


    4\!\cdot\!\sin\alpha\!\cdot\!\cos\alpha\!\cdot\!\c  os2\alpha \;=\;2\cdot\underbrace{2\!\cdot\!\sin\alpha\!\cdot  \!\cos\alpha}_{\text{This is }\sin2\alpha}\cdot\cos2\alpha

    . . . . . . . . . . . . . = \;\underbrace{2\!\cdot\!\sin2\alpha\!\cdot\!\cos2\  alpha}

    . . . . . . . . . . . . . =\qquad \sin4\alpha

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  6. #6
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    ahh i seee, thanks a lot you guys i am thinking a little too hard.
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