[Toán 11] Lượng giác

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niemkieuloveahbu

[TEX]sin^4x+cos^4(x+\frac{\pi}{4})=\frac{1}{4}\\ \Leftrightarrow (\frac{1-cos2x}{2})^2+(\frac{1+cos(2x+\frac{\pi}{4})}{2})^2=\frac{1}{4}\\\Leftrightarrow cos^22x+1-2cos2x+sin^22x+1-2sin2x=1\\ \Leftrightarrow sin2x+cos2x=1\\ \Leftrightarrow cos(2x-\frac{\pi}{4})=\frac{1}{\sqrt{2}}\\ \Leftrightarrow \[x=k\pi\\x=\frac{\pi}{4}+k\pi, k\in Z[/TEX]
 
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