A curve passes through the point $$\left(1, \frac{\pi}{6}\right).$$ Let the slope of the curve at each point (x, y) be $$\frac{y}{x} + \sec \left(\frac{y}{x}\right), x > 0.$$ Then the equation of the curve is

A

$$\sin \left(\frac{y}{x}\right) = \log x + \frac{1}{2}$$

B

$$cosec \left(\frac{y}{x}\right) = \log x + 2$$

C

$$\sec \left(\frac{2y}{x}\right) = \log + 2$$

D

$$\cos \left(\frac{2y}{x}\right) = \log x + \frac{1}{2}$$