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Math Help - deduce

  1. #1
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    deduce

    Prove that , for all values of a , sin a (cos 2a+cos 4a+cos 6a)=cos 4a sin 3a

    i can prove this ..

    Deduce that \sin \frac{\pi}{12}=\frac{1}{\sqrt{6}+\sqrt{2}}
    i am not sure with this . i don see how i can use the prove above to solve this . Thanks for your help .
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by thereddevils View Post
    Prove that , for all values of a , sin a (cos 2a+cos 4a+cos 6a)=cos 4a sin 3a

    i can prove this ..

    Deduce that \sin \frac{\pi}{12}=\frac{1}{\sqrt{6}+\sqrt{2}}
    i am not sure with this . i don see how i can use the prove above to solve this . Thanks for your help .
    \sin a=\frac{\cos\!\left(4a\right)\sin\!\left(3a\right)  }{\cos\!\left(2a\right)+\cos\!\left(4a\right)+\cos  \!\left(6a\right)}

    So \sin\tfrac{\pi}{12}=\frac{\cos\tfrac{\pi}{3}\sin\t  frac{\pi}{4}}{\cos\tfrac{\pi}{6}+\cos\tfrac{\pi}{3  }+\cos\tfrac{\pi}{2}}=\frac{\tfrac{1}{2\sqrt{2}}}{  \tfrac{\sqrt{3}}{2}+\tfrac{1}{2}}=\frac{1}{\sqrt{3  }\sqrt{2}+\sqrt{2}}=\frac{1}{\sqrt{6}+\sqrt{2}}
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