If 0 ≤ x < 2π, then the number of real values of x which satisfy the equation cosx + cos2x + cos3x + cos4x = 0

cosx + cos4x + cos2x + cos3x = 0
→ 2cos(5x/2)cos(3x/2) + 2cos(5x/2)cos(x/2) = 0
→ 2cos(5x/2)[cos(3x/2) + cos(x/2)] = 0
→ 2cos(5x/2)[2cos(x)cos(x/2)] = 0
cosx = 0 → x = π/2, 3π/2
cosx/2 = 0 → x = π
cos(5x/2) = 0 → x = π/5, 3π/5, 7π/5, 9π/5
Total number of solutions = 7