Question

The equation of the curve passing through the point (1, π/4) and tangent at any point of which makes an angle tan^-1(y/x - cos²(y/x)) is

(A) y = tan^-1[log(e/x)]

(B) y = xtan^-1(y/x) + 1

(C) y = xtan^-1(1 - logx)]

(D) y - x = tan^-1(1 - logx)

Answer 1

Answer is (C) y = xtan^-1(1 - logx)]

We have

Integrating, we get

The curve passes through (1, π/4), so c = 1 Therefore,

tan(y/x) = 1 - logx ⇒ y/x = tan^-1(1 - logx)