Prove that `(1-sintheta+costheta)^2=2(1+costheta)(1-sintheta)`

Explanation

To prove that \((1 - \sin \theta + \cos \theta)^2 = 2(1 + \cos \theta)(1 - \sin \theta)\), we will start by simplifying both sides of the equation.

### Step 1: Expand the left-hand side (LHS)
The left-hand side is \((1 - \sin \theta + \cos \theta)^2\).

Using the formula \((a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\), we can let:
- \(a = 1\)
- \(b = -\sin \theta\)
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