If for , – 1 < x < 1, prove that


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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