further Mathematics

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Let A=(cosA -sinA)
(sinA cosA)
show that
A^2=(cos2A sin2A)
(sin2A cos2A)

  • further Mathematics -

    A^2 = (cosA-sinA)^2 (sinAcosA)^2
    = (cos^2A-2sinAcosA+sin^2A)(sin^2Acos^2A)
    = (1-2sinAcosA)(1/4)(2sinAcosA)^2
    = (1/4)(1-sin2A)(sin2A)(sin2A)

    Hmmm. What if A = -pi/4?
    (1/√2 + 1/√2)(-1/√2 * 1/√2) =? (0)(0)
    -1/√2 =? 0
    Nope. I don't think it's true. Typo?

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