Question

If \(y=f(x)\) satisfies \[ \tan x \frac{dy}{dx}+(1+\tan^2 x)y=\tan x(1+\tan^2 x)^2 \] and passes through \(\left(\frac{\pi}{4},\frac{3}{4}\right)\), find \(f\left(\frac{\pi}{3}\right)\)

• A. \(\frac{5}{4\sqrt3}\)
• B. \(\frac{5\sqrt3}{4}\)
• C. \(\frac{6\sqrt3}{5}\)
• D. \(\frac{6}{5\sqrt3}\) \bigskip

Hint:

Convert everything into \(\sec^2 x\) when tan/sec appear together.

Answer 1

The Correct Option is B