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in Continuity and Differentiability by (28.2k points)
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Consider the equation

\(\sqrt{1-x^2} + \sqrt{1-y^2} = a(x-y)\)

(i) Simplify the above equation to sin-1x – sin-1y = 2cot-1 a by giving suitable substitution.

(ii) Prove that \(\frac{dy}{dx}\) = \(\sqrt{\frac{1-y^2}{1-x^2}}\)

1 Answer

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by (28.9k points)
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Best answer

(i)

Given,

(ii) We have; 

sin-1 x – cos-1y = 2cot-1a.
Differentiating w.r.t x, we get,

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