Question

The slope of the tangent at \((x,y)\) to a curve passing through \(\left(1, \frac{\pi}{4}\right)\) is given by \(\frac{y}{x} - \cos^2\left(\frac{y}{x}\right)\) then the equation of the curve is

• A. \(y = \tan^{-1}\left(\log \frac{c}{x}\right)\)
• B. \(y = x\tan^{-1}\left(\log \frac{x}{c}\right)\)
• C. \(y = x\tan^{-1}\left(\log \frac{c}{x}\right)\)
• D. None of these

Hint:

Use homogeneous substitution \(y = vx\).

Answer 1

The Correct Option is C