precal

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The values of x that are solutions to the equation cos^(2)x=sin2x in the interval [0, pi] are

a. arctan(1/2) only
b. arctan(1/2) and pi
c. arctan(1/2) and 0
d. arctan(1/2) and (pi/2)
e. arctan(1/2), o, and (pi/2)

  • precal -

    cos^2 x - sin 2x = 0 , 0 ≤ x ≤ π
    cos^2 x - 2sinxcosx= 0
    cosx(cosx - 2sinx) = 0
    cosx = 0
    x = π/2
    or
    cosx = 2sinx
    cosx/sinx = 2
    sinx/cosx = 1/2
    tanx = 1/2 , tan is positive only in I for our domain
    x = arctan(1/2)

    so it looks like D

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