Solve sin (tan^{–1} x), | x| < 1 is equal to

**(A) **`x/(sqrt(1-x^2))`

(**B) `1/sqrt(1-x^2)`**

(**C) `1/sqrt(1+x^2)`**

(**D) `x/(sqrt(1+ x^2))`**

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#### Solution

Let tan^{−1} *x* = *y*. Then, tan y = x => `sin y = x/sqrt(1+x)`

`:. y = sin^(-1) (x/(sqrt(1+x^2))) => tan^(-1) x = sin^(-1) (x/sqrt(1+ x^2))`

`:. sin (tan^(-1) x) = sin(sin^(-1) x/(sqrt(1+ x^2))) = x/sqrt(1+x^2`

The correct answer is D.

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