यदि `"tan"^(-1)(1+x)+"tan"^(-1)(1-x)=(pi)/6` तो सिद्ध कीजिए कि
`x^(2)=2sqrt(3)`

Explanation

दिया है कि
`"tan"^(-1)(1+x)+"tan"^(-1)(1-x)=(pi)/6` ltbgt `"tan"^(-1)(1+x)+"tan"^(-1)(1-x)=(pi)/6`
`"tan"^(-1)(1+x+1-x)/(1-(1+x)(1-x))=(pi)/6` [ :' "tan"^(-1)x+"tan"^(-1)y, ="tan"^(-1)((x+y)/(1-xy))]`
`"tan"^(-1)2/(1-(1-x^(2)))=(pi)/6`
`implies"tan"^(-1)(2/(1-1+x^(2))=(pi)/6`
`implies2/(x^(2))= "tan"(pi)/6=1/(sqrt(3))`
`implies2/(x^(2))=1/(sqrt(3))`
`implies x^(2)=2sqrt(3))`