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A curve passes through the point (1, π/6). Let the slope of the curve at each point (x, y) be y/x + sec(y/x), x > 0. Then the equation of the curve is -
- sin(y/x) = log x + 1/2
- cosec(y/x) = log x + 2
- sec(2y/x) = log x + 2
- cos(2y/x) = log x + 1/2
Correct answer: sin(y/x) = log x + 1/2
Solution
The slope of the curve is given as y/x + sec(y/x). By separating variables and integrating, the equation of the curve is derived as sin(y/x) = log x + 1/2, which satisfies the given conditions, including the point (1, π/6).
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