Posted by **Maurice** on Thursday, March 22, 2012 at 11:26am.

Solve each equation for all real values of x.

7.) 3 cos 2x - 5 cos x = 1

8.) 2 sin^2 x-5 sin x + 2 = 0

9.)3 sec^2 - 4 = 0

10.) tan x (tan x-1) = 0

- Math -
**Steve**, Thursday, March 22, 2012 at 12:18pm
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

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