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pre-calculus

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solve cos 2x=secx for 0(<=)x<2pi using trigonometric identities.

  • pre-calculus - ,

    Since cos(2x) = 1 at x = 0,pi,2pi,3pi,...
    sec(x) = 1 at 0,2pi,4pi,6pi,...

    They meet at even multiples of pi.

    cos never gets above 1, sec never gets below 1.

    On your interval, x=0 is the only solution

    Analytically,

    cos 2x = sec x
    2cos^2 x - 1 = 1/cosx
    2 cos^3 x - cos x - 1 = 0

    cosx = 1 is the only real solution.
    so, x=0

  • pre-calculus - ,

    cos(2theta)= 120/169; 2theta in QIV

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