ExamBro
ExamBro
COMEDK · Maths · 32. Differential Equations

The solution of the differential equation \(\left(\dfrac{d y}{d x}\right) \tan y=\sin (x+y)+\sin (x-y)\) is

  1. A \(\sec x=-2 \cos y+C\)
  2. B \(\sec y=-2 \cos x+C\)
  3. C \(\sec y=2 \cos y+C\)
  4. D \(\sec x=-2 \sec y+C\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sec y=-2 \cos x+C\)

Step-by-step Solution

Detailed explanation

The given differential equation is \(\dfrac{dy}{dx} \tan y = \sin(x+y) + \sin(x-y)\). Using the trigonometric identity \(\sin(A+B) + \sin(A-B) = 2 \sin A \cos B\), the equation becomes: \(\dfrac{dy}{dx} \tan y = 2 \sin x \cos y\). Rearranging the terms to separate the variables:…