Posted by Joe on .
Cos[x + (7 Pi)/4] + Cos[x  (7 Pi)/4] = 1

Trig/precalc 
Steve,
cos(x) cos(7pi/4)  sin(x) sin(7pi/4) + cos(x) cos(7pi/4) + sin(x) sin(7pi/4) = 1
2cos(x) cos(7pi/4) = 1
2cos(x) * 1/√2 = 1
cos(x) = 1/√2
x = pi/4 or 7pi/4