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Math Help - HELP!!lowering power in terms of the first power of cosine [(cosx)^4][(sinx)^4]

  1. #1
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    Question HELP!!lowering power in terms of the first power of cosine [(cosx)^4][(sinx)^4]

    I really got trouble w/ whole lowering powers thing! need help on this one:[(cosx)^4][(sinx)^4]
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  2. #2
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    Re: HELP!!lowering power in terms of the first power of cosine [(cosx)^4][(sinx)^4]

    $\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$

    so

    $\cos(2a)=\cos^2(a)-\sin^2(a)=2\cos^2(a)-1$

    so

    $\cos^2(a)=\dfrac{1+\cos(2a)} 2$

    You can also write

    $\cos(2a)=\cos^2(a)-\sin^2(a)=1-2\sin^2(a)$

    so

    $\sin^2(a)=\dfrac{1-\cos(2a)} 2$

    and

    $\cos^4(a)=\left(\dfrac{1+\cos(2a)} 2\right)^2$

    $\sin^4(a)=\left(\dfrac{1-\cos(2a)} 2\right)^2$
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