Find all intervals (0,2pi)

Question

2cos^2(x)+2cos(x)=0?

Answer 1

2cos²(x) + 2cosx = 0

2cosx(cosx + 1) = 0

2cosx = 0 or cosx + 1 = 0

cosx = 0 = cos(π/ 2) = cos(3π / 2)

x = π / 2 , 3π / 2 in the interval (0 , 2π)

cosx + 1 = 0

cosx = - 1 = cosπ

x = π interval (0 , 2π)

Therefore x = π / 2 , π , 3π / 2.