Give a list of solutions, in the interval [0, 360°), in degrees, of the equation 2cos^24θ + 5 cos 4θ = 3.

Answer 1

your equation is
(2cos4θ - 1)(cos4θ + 3) = 0
so, find all the angles θ where

cos4θ = 1/2 or cos4θ = -3

Note that cos4θ has period pi/2, so you will have more solutions than normal, since the domain covers 4 periods.