Question

Which of the following are solutions to the equation 2cos^2(x) - 1 = 0? Check all that apply.

A. 3pi/4
B. 15pi/4
C. pi/8
D. -7/pi/4

Answer 1

A. 3pi/4

B. 15pi/4

D. -7/pi/4

Explanation:

cos2x=0

2x= pi/2 and 3pi/2

x=pi/4 and 3pi/4

All solutions will be multiples of pi/4

Answer 2

The equation 2cos^2(x) - 1 = 0 we manupulate by adding 1 to both sides and then dividing both sides by 2.
2cos^2(x) - 1 = 0
2cos^2(x) = 1
cos^2(x) = 1/2
cos(x) = ±√1/2
cos(x) = ±√(2)/2
The answers to your question are A. 3pi/4, B. 15pi/4, and D. -7pi/4 as they all are angles with a reference angle of pi/4. They will have a cosine ratio of √(2)/2 or -√(2)/2