Express `sin^(-1).(sqrtx)/(sqrt(x + a))` as a function of `tan^(-1)`

1.	Express `sin^(-1).(sqrtx)/(sqrt(x + a))` as a function of `tan^(-1)`
Answer» Correct Answer - `tan^(-1) (sqrt((x)/(a)))` Putting `x = a tan^(2) theta` `:. Sin.^(-1) (sqrtx)/(sqrt(x + a) = sin^(-1) (sqrta sqrt(tan^(2)theta))/(sqrt(a tan^(2) theta + a))` `= sin.^(-1) (sqrta tan theta)/(sqrta sec theta)` `= sin^(-1) sin theta = theta = tan^(-1) (sqrt((x)/(a)))`

Discussion

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