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Express sin^(-1)((sin x+ cos x)/(sqrt2))...

Express `sin^(-1)((sin x+ cos x)/(sqrt2))`, where `-(pi)/(4) lt x lt (pi)/(4)`, in the simplest form.

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To express \( \sin^{-1}\left(\frac{\sin x + \cos x}{\sqrt{2}}\right) \) in its simplest form, we will follow these steps: ### Step 1: Rewrite the expression We start with the expression: \[ y = \sin^{-1}\left(\frac{\sin x + \cos x}{\sqrt{2}}\right) \] ...
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