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If tan(cos^(-1) x) = sin (cot^(-1).(1)/(...

If `tan(cos^(-1) x) = sin (cot^(-1).(1)/(2))`, then find the value of x

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The correct Answer is:
`x = (sqrt5)/(3)`
`tan (cos^(-1) x) = sin (cot.^(-1) (1)/(2))`
`rArr tan (tan^(-1) ((sqrt(1 - x^(2)))/(x)) = sin (sin.^(-1) ((2)/(sqrt5)))` ltrbgt or `(sqrt(1 - x^(2)))/(x) = (2)/(sqrt5)`
or `4x^(2) = 5 - 5 x^(2)`
or `x = (sqrt5)/(3) " " [ :' x = (-sqrt5)/(3), L.H.S. lt 0 " but " R.H.S. gt 0]`
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