If `y=sqrt(cosx+sqrt(cosx+sqrt(cosx+\ dotto\ oo)))` , prove that `(dy)/(dx)=(sinx)/(1-2y)` .

Explanation

To solve the problem, we start with the given equation:

\[ y = \sqrt{\cos x + \sqrt{\cos x + \sqrt{\cos x + \cdots}}} \]

### Step 1: Rewrite the equation
Notice that the expression inside the square root is the same as \( y \). Therefore, we can rewrite the equation as:

\[ y = \sqrt{\cos x + y} \]
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