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Math Help - Simplifying (sin2x)(-sin2x)

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    Simplifying (sin2x)(-sin2x)

    The equation is (1-sin2x)(1+sin2x) = 1+sin2x-sin2x- (sin2x)(sin2x)
    Does that equal = 1 - 2sin2x or 1 - (sin2x)^2 = 1- sin4x^2 ?? I have not done this before
    Last edited by sakonpure6; November 25th 2013 at 03:04 PM.
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    Re: Simplifying (sin2x)(-sin2x)

    Quote Originally Posted by sakonpure6 View Post
    The equation is (1-sin2x)(1+sin2x) = 1+sin2x-sin2x- (sin2x)(sin2x)
    Does that equal = 1 - 2sin2x or 1 - (sin2x)^2 = 1- sin4x^2 ?? I have not done this before
    None of can answer what we cannot read.

    Do you mean 1) (\sin(2x))(-\sin(2x)) or do you mean 2) (\sin^2(x))(-\sin^2(x))?

    Please, please learn to post correctly. Please respond with clarification.
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    Senior Member sakonpure6's Avatar
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    Re: Simplifying (sin2x)(-sin2x)

    Sorry, here is the proper equation

    (1+\sin(2x)) (1-\sin(2x))
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    Re: Simplifying (sin2x)(-sin2x)

    It would be very strange to be given problems like this involving sine if you have never taken an algebra class. But if you have taken algebra then surely you should know that (a+ b)(a- b)= a^2+ ab- ab- b^2= a^2- b^2. So (1- sin(2x))(1+ sin(2x))= 1- sin^2(2x). No, the square does does NOT apply to the argument, 2x, of the sine, it applies to the sine itself.
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    Re: Simplifying (sin2x)(-sin2x)

    Quote Originally Posted by HallsofIvy View Post
    It would be very strange to be given problems like this involving sine if you have never taken an algebra class. But if you have taken algebra then surely you should know that (a+ b)(a- b)= a^2+ ab- ab- b^2= a^2- b^2. So (1- sin(2x))(1+ sin(2x))= 1- sin^2(2x). No, the square does does NOT apply to the argument, 2x, of the sine, it applies to the sine itself.
    OMG I Love you!!!!!!! You just helped me solve an identity that took me forever!!!!!!!!!!!!!!!!!!!!!!!!!!

    (1-sin2x)/(cos2x) = (cos2x)/(1+sin2x)
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