The general solution of the differential equation $\cos (x+y) d y=d x$ is

• Correct answer
  A

  $y=\tan \left(\frac{x+y}{2}\right)+c$
• B

  $y=\sec \left(\frac{x+y}{2}\right)+c$
• C

  $y=x \sec \left(\frac{y}{x}\right)+c$
• D

  $y=-\cos ^{-1}\left(\frac{y}{x}\right)+c$

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