Solve the equations.`sin(tan^(-1)x),|x|<1`
(A) `x/(sqrt(1-x^2))`
(B) `1/(sqrt(1-x^2))`
(C) `1/(sqrt(1+x^2))`
(D) `x/(sqrt(1+x^2))`

Explanation

To solve the equation \( \sin(\tan^{-1} x) \) for \( |x| < 1 \), we can follow these steps:

### Step 1: Define the angle
Let \( \theta = \tan^{-1}(x) \). By definition of the inverse tangent function, we have:
\[ \tan(\theta) = x \]

...