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in Continuity and Differentiability by (28.9k points)
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If y = \(\frac{sin^{-1}x}{\sqrt{1-x^2}}\) prove that
(i) (1 – x2) y2 = (sin-1x)2 
(ii) (1 – x2)y1 – xy = 1 
(iii) (1 – x2) y2 – 3xy1 – y = 0

1 Answer

+1 vote
by (28.2k points)
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Best answer

 (i) 

(ii) Differentiating

(1 – x2) 2y.y1 + y2x – 2x = \(\frac{2sin^{-1}x}{\sqrt{1-x^2}}\)

(1 – x2)2yy1 – 2xy2 = 2y
(1 – x2) y1 – xy = 1.

(iii) Again differentiating
(1 – x2) y2 + y1 x – 2x – xy1 – y = 0
(1 – x2) y2 – 3xy1 – y = 0.

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