[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]