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Solve |sinx +cos x |=|sinx|+|cosx|, x in...

Solve `|sinx +cos x |=|sinx|+|cosx|, x in [0,2pi]`.

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To solve the equation \( | \sin x + \cos x | = | \sin x | + | \cos x | \) for \( x \) in the interval \( [0, 2\pi] \), we will analyze the conditions under which the equality holds. ### Step 1: Understand the absolute value condition The equation \( | \sin x + \cos x | = | \sin x | + | \cos x | \) holds true under certain conditions: 1. Both \( \sin x \) and \( \cos x \) are non-negative. 2. Both \( \sin x \) and \( \cos x \) are non-positive. 3. One of them is zero. ...
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