If `sin^(-1)((x^2-y^2)/(x^2+y^2))=logat h e n(dy)/(dx)`is equal to `(x^2-y^2)/(x^2+y^2)` (b) `y/x` (c) `x/y` (d) none of these

Explanation

`frac{x^{2}-y^{2}}{x^{2}+y^{2}}=sin (log a)=lambda[ sin (log a) text { is constant }] `


`x^{2}-y^{2}=lambda(x^{2}+y^{2})=lambda x^{2}+lambda y^{2} `


`therefore x^{2}(1-lambda)=y^{2}(1+lambda) quad ldots(1)`


`Rightarrow 2 x(1-lambda)=2 y frac{d y}{d x}(1+lambda)`



Dividing `(2)` by `(1)`, we have



`frac{2}{x}=frac{2}{y} frac{d y}{d x} Rightarrow frac{d y}{d x}=frac{y}{x}`