If `f(x)=(2x)/(1+x^2)\ ,` show that `f(tantheta)=sin2theta)`

Explanation

To show that \( f(\tan \theta) = \sin 2\theta \) for the function \( f(x) = \frac{2x}{1 + x^2} \), we will follow these steps:

### Step 1: Substitute \( x \) with \( \tan \theta \) in the function
We start with the function:
\[ f(x) = \frac{2x}{1 + x^2} \]
Now, we replace \( x \) with \( \tan \theta \):
...