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) $\quad \sin \left( \frac { y } { x } \right) = \log x + \frac { 1 } { 2 }$ (B) $\quad \operatorname { cosec } \left( \frac { y } { x } \right) = \log x + 2$ (C) $\quad \sec \left( \frac { 2 y } { x } \right) = \log x + 2$ (D) $\quad \cos \left( \frac { 2 y } { x } \right) = \log x + \frac { 1 } { 2 }$
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) $\quad \sin \left( \frac { y } { x } \right) = \log x + \frac { 1 } { 2 }$\\
(B) $\quad \operatorname { cosec } \left( \frac { y } { x } \right) = \log x + 2$\\
(C) $\quad \sec \left( \frac { 2 y } { x } \right) = \log x + 2$\\
(D) $\quad \cos \left( \frac { 2 y } { x } \right) = \log x + \frac { 1 } { 2 }$