Find all solutions to the equation cosx pi2 cosx pi2 squ

Find all solutions to the equation cos(x + pi/2) - cos(x - pi/2) = -squareroot 2 Write your answer in radians in terms of pi, and use the or button Example: x = pi/5 + 2k pi, k element of Z or x = pi/7 + k pi, k element of Z

Solution

cos(/2+x) - cos(/2-x) = -2

=> -sinx -sinx = -2

=> -2sinx = -2

=> sinx = 1/2

=> x = [(5n+1)/2] + /4 or x =[(5n+1)/2] - /4