If `sinx+cosx=sqrt(y+1/y)` for `x in [0,pi]` , then (a) `x=pi/4` (b) `y=0` (c) `y=1` (d) `x=(3pi)/4`

Explanation

To solve the equation \( \sin x + \cos x = \sqrt{y + \frac{1}{y}} \) for \( x \) in the interval \([0, \pi]\), we will analyze both sides of the equation step by step.

### Step 1: Rewrite the Left-Hand Side
We start with the left-hand side:
\[ \sin x + \cos x \]
We can express this as:
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