Question

If cosx=sqrt(1/2 + 1/(2sqrt(2))) and sinx=-sqrt(1/2 - 1/(2sqrt(2))) with 0 <= x < 2pi , it follows that 2x = kpi. The value of k is:

Answer 1

since cos(x) = √((1+cos2x)/2) = √((1 + 1/√2)/2) = √((1 + cosπ/4)/2)
it follows that 2x = π/4 so k = 1/4