The correct option is A 1
Put x2=sinα,y2=sinβ
∴ Given equation reduces to cosα+cosβ=a(sinα−sinβ)
⇒2cos(α+β2)cos(α−β2)=2acos(α+β2)sin(α−β2)
⇒cot(α−β2)=a
⇒α−β=2cot−1a
⇒sin−1x2−sin−1y2=2cot−1a
On differentiating w.r.t. x, we get
1√1−x4.2x−1√1−y4.2ydydx=0⇒dydx=xy√1−y41−x4
Which is a differential equation of first order and first degree.
Hence, (A) is the correct answer