$\rm sin(a+b)=sina.cosb+cosa.sinb$

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$\rm sinx+cosx=\sqrt2 . sin (x+\dfrac{\pi}{4})$

$\rm VP: \sqrt2 . sin (x+\dfrac{\pi}{4})$

$\rm =\sqrt2 . (sinx.cos \dfrac{\pi}{4}+cosa.sin \dfrac{\pi}{4})$

$\rm =\sqrt2 . ( sinx. \dfrac{\sqrt2}{2} + cos x.\dfrac{\sqrt2}{2} )$

$\rm =\sqrt2 . \dfrac{\sqrt2}{2} .( sinx+cosx)$

$\rm =sinx+cosx ( =VT )$ (đpcm)