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Questions Asked in Previous 10 Years' Exams
A curve passes through the point \( \left(1, \frac{\pi}{6}\right) \). Let the slope of the curve at each point \( (x, y) \) be \( \frac{y}{x}+\sec \left(\frac{y}{x}\right), x0 \). Then, the equation of the curve is [Only One Correct 2013]
(a) \( \sin \left(\frac{y}{x}\right)=\log x+\frac{1}{2} \)
(b) \( \operatorname{cosec}\left(\frac{y}{x}\right)=\log x+2 \)
(c) \( \sec \left(\frac{2 y}{x}\right)=\log x+2 \)
(d) \( \cos \left(\frac{2 y}{x}\right)=\log x+\frac{1}{2} \)
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