If tan-1 [ (x2 - y2)/ (x2 + y2) ] = a ; prove that dy/dx = x( 1 - tanA) / y ( 1 + tanA)

Given that,tan-1x2-y2x2+y2=ax2-y2x2+y2=tanaDifferentiating on both side w.r.t. x,we have,ddxx2-y2x2+y2=ddxtanax2+y2ddxx2-y2-x2-y2ddxx2+y2x2+y22=0x2+y22x-2ydydx-x2-y22x+2ydydx=02xx2+y2-2yx2+y2dydx-2xx2-y2-2yx2-y2dydx=0xx2+y2-yx2+y2dydx-xx2-y2-yx2-y2dydx=0yx2-y2+yx2+y2dydx=xx2+y2-xx2-y2dydx=xx2+y2-xx2-y2yx2-y2+yx2+y2dydx=x-xx2-y2x2+y2yx2-y2x2+y2+ydydx=x-xtanaytana+ydydx=x1-tanay1+tanaHence Proved.

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