Math
posted by Maurice on .
Solve each equation for all real values of x.
7.) 3 cos 2x  5 cos x = 1
8.) 2 sin^2 x5 sin x + 2 = 0
9.)3 sec^2  4 = 0
10.) tan x (tan x1) = 0

7)
since cos 2x = 2cos^2 x  1, we have
6cos^2 x  5cos x  4 = 0
(2cos x + 1)(3cos x  4) = 0
cos x = 1/2 > x = 2pi/3 or 5pi/3
cos x = 4/3 > no solution
8)
(sin x  2)(2sin x  1) = 0
sin x = 2 > no solution
sin x = 1/2 > x = pi/6 or 5pi/6
9)
3sec^2 x = 4
sec x = ±2/√3
or, more familiarly,
cos x = ±√3/2
x = pi/6, 5pi/6, 7pi/6, 11pi/6
10)
tan X = 0 > x = 0, pi
tan x = 1 > x = pi/4, 5pi/4