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Math Help - Prove this identity?

  1. #1
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    Prove this identity?

    Can someone please help me solve this identity? I need all steps. I really just do not understand it :/

    thank you !




    sin^4 β - cos^4 β = 1 - 2cos^2 β
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  2. #2
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    I mean *PROVE this identity.
    using trigonometric identities :|
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by dlngoal View Post
    Can someone please help me solve this identity? I need all steps. I really just do not understand it :/

    thank you !




    sin^4 β - cos^4 β = 1 - 2cos^2 β
     (sin^{4}\beta) - (cos^{4}\beta)

     = {(sin^{2}\beta)^2} -{(cos^{2}\beta)^2}

    = (sin^{2}\beta + cos^{2}\beta) \times (sin^{2}\beta - cos^{2}\beta) [ Note: (a^2-b^2) = (a+b)(a-b) ]

    = 1 \times (sin^{2}\beta - cos^{2}\beta) [      Note: sin^{2}x+cos^{2}x = 1]

    = [(1-cos^{2}\beta) -cos^{2}\beta]     [Note: sin^{2}x = 1 - cos^{2}x]

    = 1 - 2cos^{2}\beta
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  4. #4
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    You are a life saver thank youu
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  5. #5
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by dlngoal View Post
    You are a life saver thank youu
    haha! Am I really?
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  6. #6
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    Yess! You are! haha
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