Maths

If tan inverse(x^2-y^2/x^2+y^2)=a then prove that dy/dx=x/y (1-tana/1+tana).

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  1. Hint:
    write equation as:
    tan(a)=(x²-y²)/(x²+y²)
    Cross multiply to eliminate denominators:
    (x²+y²)tan(a)=(x²-y²)
    Implicitly differentiate both sides
    (2x+2yy')tan(a) = 2x-2yy'
    Group terms and express y'(=dy/dx) in terms of x, y and tan(a) to get the required expression.

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  2. Thanku soo much

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