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Please do this differentiation. √1-x^4+√1-y^4=k(x^2-y^2)

Please do this differentiation. √1-x^4+√1-y^4=k(x^2-y^2)

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Grade:12

1 Answers

Mayukh Chakrabarty
56 Points
3 years ago
To solve this assume x²=sin py²=sin qPut these values and simplify using trigonometric identities (formulae for cos A + cos B and sin A - sin B are needed) to reduce the expression to1/k = tan ((p-q)/2)On rearrangement it becomesp-q = 2 tan inverse (1/k) = constant (say c)Substitute p = sin inverse x² and q = sin inverse y² and differentiate .RHS being constant turns 0LHS becomes {2x/√(1-x²)} - {2y/√(1-y²)}(dy/dx)Now rearrange to get the result .

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