giai phuong trinh: $sin3x + cos3x + cosx - sinx = \sqrt{2}cos2x$

           ( Dung cong thuc goc nhan 3 giup minh nha)
Cách kia nhanh hơn nhưng chính bạn muốn dùng nhân 3 đấy nhá, ừ thì chơi nhân 3 cho nó máu

$3\sin x - 4\sin^3 x + 4\cos^3 x-3\cos x-\sin x + \cos x = \sqrt2(\cos x - \sin x)(\cos x + \sin x)$

$\Leftrightarrow -4(\sin^3 x-\cos^3 x)+2\sin x - 2\cos x=-\sqrt2(\sin x - \cos x)(\sin x+\cos x)$

$\Leftrightarrow -4(\sin x-\cos x)(1+\sin x \cos x)+2(\sin x - \cos x)+\sqrt2(\sin x - \cos x)(\sin x + \cos x)=0$

$\Leftrightarrow (\sin x -\cos x)[\sqrt2(\sin x+cosx)-4\sin x \cos x-2]=0$

Dễ rồi nha
$PT \Leftrightarrow (sin3x-sinx) + (cos3x+cosx)=\sqrt2cos2x$

$\Leftrightarrow 2cos2xsinx+2cos2xcosx=\sqrt2cos2x$

$\Leftrightarrow cos2x(sinx+cosx-\sqrt2)=0$

Còn lại khá dễ nên bạn tự giải nha
Nếu đúng bạn nhấn V để chấp nhận, mũi tên để vote up cho đáp án của mình nha. Cảm ơn :) –  NguyễnTốngKhánhLinh 24-07-13 09:25 PM

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