If `sin^(-1)x + tan ^(-1) x = (pi)/(2)`, then prove that `2x^(2) + 1 = sqrt(5)`

If `sin^(-1)x + tan ^(-1) x = (pi)/(2)`, then prove that `2x^(2) + 1 =

1.	If `sin^(-1)x + tan ^(-1) x = (pi)/(2)`, then prove that `2x^(2) + 1 = sqrt(5)`
Answer» ` sin^(-1) x + tan ^(-1) x =(pi)/(2)` ` rArr tan^(-1) x =(pi)/(2)- sin^(-1) x` `" "=cos^(-1)x = tan^(-1).(sqrt(1-x^(2)))/(x)` `rArr " "x=sqrt(1-x^(2))/(x)` `rArr" " x^(2) = sqrt(1-x^(2))` `" "x^(4)+x^(2) -1= 0` `rArr " "x^(2)=(-1pmsqrt(1+4))/(2xx1)` `rArr " "2x^(2) = -1 pm sqrt(5)` `rArr " " 2x^(2) + 1 = sqrt(5)` `" "(because 2x^(2)+ 1 = - sqrt(5)" is not possible")`

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