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Math Help - how does this happen?

  1. #1
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    how does this happen?

    sqrt(4 - (2sinx)^2)2cosx = 4cos^2(x)

    There are steps in the middle (obviously) but I can't figure them out
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  2. #2
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    Quote Originally Posted by TYTY View Post
    sqrt(4 - (2sinx)^2)2cosx = 4cos^2(x)

    There are steps in the middle (obviously) but I can't figure them out
    I can see why you are having trouble: the statement is not an identity. For example, with x=\pi, the left-hand side is 2(-2)=-4, but the right-hand side is 4(-1)^2=4. We can, however, show that the two expressions differ only in sign:

    2\cos x\sqrt{4-(2\sin x)^2}

    =2\cos x\sqrt{4-4\sin^2x}

    =2\cos x\sqrt{4\left(1-\sin^2x\right)}

    =4\cos x\sqrt{1-\sin^2x}

    =4\cos x\sqrt{\cos^2x}

    =4\cos x|\cos x|

    =\pm4\cos^2x
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  3. #3
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    This is very helpful and I appreciate it
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