Question

यदि `sin^(-1)x+tan^(-1)x=(pi)/(2)` तो सिद्ध कीजिए कि `2x^(2)+1=sqrt5`

Answer 1

`impliestan^(-1)x=(pi)/(2)-sin^(-1)x=cos^(-1)x=tan^(-1)""(sqrt(1-x^(2)))/(x)`
`impliesx=(sqrt(1-x^(2)))/(x)" implies "x^(2)=sqrt(1-x^(2))`
`x^(4)=1-x^(2)" implies "x^(4)+x^(2)-1=0`
`impliesx^(2)=(-1+-sqrt(1+4))/(2xx1)" implies "2x^(2)=-1+-sqrt5`
`implies2x^(2)+1=sqrt5(":.2x^(2)+1=-sqrt5` सम्भव नहीं है।)