If $\cos x \frac{d y}{d x}=y \sin x-1, x \neq(2 n+1) \frac{\pi}{2}, n \in \mathrm{Z}$ is the differential equation corresponding to the curve $y=f(x)$ and $f(0)=1$ then $f(x)=$

• Correct answer
  A

  $(1-x) \sec x$
• B

  $(1-x) \cos x$
• C

  $x+\cos x$
• D

  $x+\sec x$

Hence, the correct answer is option: 'A'.