If cosx(dy/dx) - ysinx = 6x, (0 < x < π/2) and y(π/3) = 0, then y(π/6) is equal to:

The correct option is C -π/2√3
dy/dx - ytanx = 6xsecx
y(π/3) = 0; y(π/6) = ?
Let p = ycosx
dp/dx = (dy/dx)cosx - ysinx
dp/dx = 6x
p = ∫6xdx = 3x² + C
ycosx = 3x² + C
When x = π/3, y = 0
0 = 3(π/3)² + C
0 = π²/3 + C
C = -π²/3
ycosx = 3x² - π²/3
y = (3x² - π²/3)secx
For x = π/6
y(π/6) = (3(π/6)² - π²/3)sec(π/6)
= (3π²/36 - π²/3)(2)
= (π²/12 - 4π²/12)(2)
= (-3π²/12)(2)
= (-π²/4)(2)
= -π²/2
= -π/2√3