If `sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"f i n d"(dy)/(dx)dot`

Explanation

To find \(\frac{dy}{dx}\) given the equations \( \sin x = \frac{2t}{1+t^2} \) and \( \tan y = \frac{2t}{1-t^2} \), we will follow these steps:

### Step 1: Express \(x\) in terms of \(t\)
From the equation \( \sin x = \frac{2t}{1+t^2} \), we can recognize that this is the formula for \(\sin 2\theta\) where \(t = \tan \theta\). Thus, we can write:

\[ \sin x = \sin(2\theta) \]
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