Question

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

Answer 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.

Answer 2

Thanku soo much