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math-trigonometry

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I'm working woith multiple ange and product sum formulas and I'm stuck on these. Can you help? Thanks

sin2xsinx=cosx

cos2x-cosx=0

  • math-trigonometry -

    are we solving?

    1st one:
    sin2xsinx=cosx
    2sinxcosxsinx - cosx = 0
    cosx(2sin^2 x - 1) = 0
    cosx = 0 or sin^2x = 1/2

    if cosx=0,
    x = π/2 or x=3π/2 (90° or 270°)

    if sin^2x = 1/2
    sinx = ±1/2
    x = π/4 , 3π/4, 5π/4, or 7π/4 (45°, 135°, 225° or 315°)

    for the 2nd
    use cos 2x = 2cos^2x - 1 to end up with a quadratic.
    give it a try.
    it will factor

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