question_answer

If the gradient of the tangent at any point (x, y) of a curve which passes through the point \[\left( 1,\frac{\pi }{4} \right)\] is \[\left\{ \frac{y}{x}-{{\sin }^{2}}\left( \frac{y}{x} \right) \right\},\]the equation of the curve will be

A)  \[y={{\cot }^{-1}}({{\log }_{e}}x)\]   

B)  \[y={{\cot }^{-1}}\left( {{\log }_{e}}\frac{x}{e} \right)\]

C)  \[y=x\,\,{{\cot }^{-1}}({{\log }_{e}}ex)\]        

D)  \[y={{\cot }^{-1}}\left( {{\log }_{e}}\frac{e}{x} \right)\]

E)  None of these