Chủ đề này có 1 trả lời

[khuyenkyu]

Gpt : $4sin^{2}5x - 4sin^{2}x + 2(sin6x + sin4x ) + 1 = 0$

[ChiLanA0K48]

Gpt : $4sin^{2}5x - 4sin^{2}x + 2(sin6x + sin4x ) + 1 = 0$

 

$\Leftrightarrow 4sin^{2}5x+4sin5x.cosx+cos^{2}x=3sin^{2}x$

$\Leftrightarrow (2sin5x+cosx)^{2}=3sin^{2}x$

$\Leftrightarrow 2sinx+cosx=\pm \sqrt{3}sinx$

 

TH1:$2sinx+cosx=\sqrt{3}sinx$

$\Leftrightarrow \frac{\sqrt{3}}{2}sinx-\frac{1}{2}cosx=sin5x$

$\Leftrightarrow sin\left ( x-\frac{\Pi }{6} \right )=sin5x$

 

TH2: $2sin5x+cosx=-\sqrt{3}sinx$

$\Leftrightarrow \frac{-\sqrt{3}}{2}sinx-\frac{1}{2}cosx=sin5x$

$\Leftrightarrow sin\left ( x-\frac{5\Pi }{6} \right )=sin5x$