1.

If `cos^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=tan^(-1)a`, prove than `(dy)/(dx)=(y)/(x).`

Answer» `(x^(2)-y^(2))/(x^(2)+y^(2))=cos [tan^(-1)a]=" constant"`
`rArr(d)/(dx)((x^(2)-y^(2))/(x^(2)+y^(2)))=0`
`rArr((x^(2)+y^(2)).(d)/(dx)(x^(2)-y^(2))-(x^(2)-y^(2)).(d)/(dx)(x^(2)+y^(2)))/((x^(2)+y^(2))^(2))=0`
`rArr(x^(2)+y^(2))[2x-2y(dy)/(dx)]-(x^(2)-y^(2))(2x+2y(dy)/(dx))=0`
`rArrx{(x^(2)+y^(2))-(x^(2)-y^(2))}=y{(x^(2)=y^(2))+(x^(2)+y^(2))}(dy)/(dx).`
Hence, `(dy)/(dx)=(y)/(x).`


Discussion

No Comment Found

Related InterviewSolutions