Question

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)

Answer 1

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