Q29 of 43 Page 5

If for , – 1 < x < 1, prove that   (CBSE 2012)

Given,



Now, squaring both sides, we get


⇒


⇒


⇒ x2 + x2y = y2 + y2x


⇒ x2 – y2 = xy2 – x2y


⇒ (x + y)(x – y) = xy (y – x)


⇒ x + y = –xy


⇒ y + xy = –x


⇒ y (1 + x) = –x


⇒


Differentiating both sides with respect to x, we get



Using Quotient Rule



∴


Hence, Proved

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