căn 2 ( cosx+sinx) = 1/2sin2x ai làm ơn giúp mk với

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1. $\begin{array}{l}
   Dat\,\sin x + \cos x = t\left( {0 \le t \le \sqrt 2 } \right)\\
   \Rightarrow {t^2} = 1 + 2\sin x\cos x = 1 + \sin 2x \Rightarrow \sin 2x = {t^2} – 1\\
   \Rightarrow \sqrt 2 t = \frac{1}{2}.\left( {{t^2} – 1} \right) \Leftrightarrow {t^2} – 2\sqrt 2 t – 1 = 0\\
   \Leftrightarrow \left[ \begin{array}{l}
   t = \sqrt 2 + \sqrt 3 \left( {loai} \right)\\
   t = \sqrt 2 – \sqrt 3 \left( {TM} \right)
   \end{array} \right. \Rightarrow \sin x + \cos x = \sqrt 2 – \sqrt 3 \\
   \Leftrightarrow \sqrt 2 \sin \left( {x + \frac{\pi }{4}} \right) = \sqrt 2 – \sqrt 3 \Leftrightarrow \sin \left( {x + \frac{\pi }{4}} \right) = \frac{{\sqrt 2 – \sqrt 3 }}{{\sqrt 2 }}\\
   \Leftrightarrow \left[ \begin{array}{l}
   x + \frac{\pi }{4} = \arcsin \frac{{\sqrt 2 – \sqrt 3 }}{{\sqrt 2 }} + k2\pi \\
   x + \frac{\pi }{4} = \pi – \arcsin \frac{{\sqrt 2 – \sqrt 3 }}{{\sqrt 2 }} + k2\pi
   \end{array} \right.\\
   \Leftrightarrow \left[ \begin{array}{l}
   x = \arcsin \frac{{\sqrt 2 – \sqrt 3 }}{{\sqrt 2 }} – \frac{\pi }{4} + k2\pi \\
   x = \frac{{3\pi }}{4} – \arcsin \frac{{\sqrt 2 – \sqrt 3 }}{{\sqrt 2 }} + k2\pi
   \end{array} \right.
   \end{array}$

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