giai phuong trinh.

B

braga

[TEX]\text{(2cosx -1)(sinx+cosx)=sin^2x+ cos^2x}[/TEX]
[TEX]\Leftrightarrow \text{2cosx.sinx + 2cos^2x - (sinx + cosx) = sin^2x + cos^2x}[/TEX]
[TEX]\Leftrightarrow \text{sin2x + (cos^2x - sin^2x) = sinx + cosx}[/TEX]
[TEX]\Leftrightarrow \text{sin2x + cos2x = sinx + cosx}[/TEX]
[TEX]\Leftrightarrow \text{sin(2x + \frac{\pi}{4}) = sin(x + \frac{\pi}{4})}[/TEX]
 
H

hocmaitlh

[TEX] (2cosx-1)(sinx+cosx)=1 [/TEX]
[TEX]\Leftrightarrow sin2x+2cos^2x-sinx-cosx=1 [/TEX]
[TEX]\Leftrightarrow sin2x+cos^2x-sin^2x=sinx+cosx [/TEX]
[TEX]\Leftrightarrow sin2x+cos2x=sinx+cosx [/TEX]
[TEX]\Leftrightarrow sin(2x+pi/4)=sin(x+pi/4) [/TEX]
 
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