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 <span> cos^2(x) = 1/2 </span> cos(x) = ±√1/2 <span> cos(x) = ±√(2)/2 </span> The answers to your question are <span>A. 3pi/4, B. 15pi/4, and D. </span>-7pi/4 as they all are angles with a reference angle of pi/4. They will have a cosine ratio of <span>√(2)/2 or </span><span><span>-</span>√(2)/2</span>