InterviewSolution
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InterviewSolution
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If `sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx)`is equal to`x/y`(b) `y/(x^2)``(x^2-y^2)/(x^2+y^2)`(d) `y/x`A. `(x)/(y)`B. `(y)/(x^(2))`C. `(x^(2)-y^(2))/(x^(2)+y^(2))`D. `(y)/(x)` |
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Answer» `"We have "sin^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=log a` `"or "(x^(2)-y^(2))/(x^(2)+y^(2))=sin (log a)` `"or "(1-tan^(2)theta)/(1+tan^(2)theta)=sin(log a)" "("on putting "y= x tan theta)` `"or "cos 2theta= sin (log a)` `"or "2theta=cos^(-1)(sin (log a))` `"or "theta=(1)/(2)cos^(-1)(sin (log a))` `"or "tan^(-1)((y)/(x))=(1)/(2)cos^(-1)(sin (log a))` `"or "(y)/(x)=tan ((1)/(2)cos^(-1)(sin (loga )))` Differentiating w.r.t. x, we get `(x(dy)/(dx)-y)/(x^(2))=0` `"or "x(dy)/(dx)-y=0` `"or "(dy)/(dx)=(y)/(x)` |
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