Question

Solve karo bhai .... This is just taking time...

Answer 1

Answer:

Step-by-step explanation:

√1 - x² + √1 - y² = a(x - y); find dy/dx = ?

Let x = SinA & y = SinB

=> √1-(SinA)² +√1-(SinB)²=a(SinA-SinB)

=> √Cos²A + √Cos²B = a(SinA-SinB)

=> CosA + CosB = a(SinA - SinB)

=> 2Cos(A+B/2).Cos(A-B/2) = a . 2Cos(A+B/2)Sin(A-B/2)

=> Cos(A-B/2) = a . Sin(A-B/2)

=> Cot (A-B/2) = a

=> A - B/2 = Cot⁻¹ a

=> A - B = 2Cot⁻¹ a

//we have assumed that x = SinA => A = Sin⁻¹(x); y = SinB => B =Sin⁻¹(y)

=> Sin⁻¹(x) - Sin⁻¹(y) = 2Cot⁻¹a

//Now differentiate w.r.t  x

=> d/dx(Sin⁻¹(x)) - d/dx(Sin⁻¹(y)) = d/dx(2Cot⁻¹a)

=> 1/√(1-x²) - 1/√(1-y²) . dy/dx = 0

=> 1/√(1-x²) = 1/√(1-y²) . dy/dx

=> dy/dx = √(1-y²)/√(1-x²)

= √[(1 - y²) / (1 - x²)]

1/√(1-y²) . dy/dx = 1/√(1-x²)

dy/dx = √(1-y²)/√(1-x²)

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