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Answer 1

Answer:

Given :

√1-x² +√1-y²=a(x-y)

To Prove :

dy/dx=√(1-y²)/(1-x²)

Solution :

√1-x² +√1-y²=a(x-y)

•Let x = sinA & y = sinB

•√1-(sinA)² +√1-(sinB)²=a(sinA-sinB)

√cos²A + √cos²B = a(sinA-sinB)

cosA + cosB = a(cosA-cosB)

•2cos[(A+B)/2 ]cos[(A-B)/2] = 2acos[(A+B)/2 ]sin[(A-B)/2]

•cos(A-B)/2 = asin(A+B)/2

[cos(A-B)/2]/sin[(A-B)/2] = a

•cot(A-B)/2 = a

(•A-B)/2 = cot^-1a

A - B = 2cot^-1(a)

•sin^-1(x) - sin^-1(y) = 2cot^-1(a)

•Differentiating both sides

1/√(1-x²) - 1/√(1-y²) . dy/dx = 0

1/√(1-y²) . dy/dx = 1/√(1-x²)

dy/dx = √(1-y²)/√(1-x²)

Hence, proved

Step-by-step explanation:

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Answer 2

Answer:

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