PT Lượng giác

T

trantien.hocmai

$$4\sin 2x.\sin x+2\sin 2x-2\sin x=4\sin ^2x \\
\leftrightarrow 2\sin 2x(2\sin x+1)=4\sin ^2x+2\sin x \\
\leftrightarrow 2\sin 2x(2\sin x+1)=2\sin x(2\sin x+1) \\
\leftrightarrow (\sin 2x-\sin x)(2\sin x+1)=0 \\
\leftrightarrow \left[ \begin{array}{I} \sin 2x=\sin x \\ 2\sin x=-1 \end{array} \right. \\
\leftrightarrow \left[ \begin{array}{I} \cos x=\dfrac{1}{2} \\ \sin x=-\dfrac{1}{2} \end{array}\right. \\
\leftrightarrow \left[ \begin{array}{I} x=\pm \dfrac{\pi}{3}+k2\pi \\ \left[ \begin{array}{I} x=-\dfrac{\pi}{6}+k2\pi \\ x=\dfrac{7\pi}{6}+k2\pi \end{array} \right. \end{array} \right.$$
 
T

trantien.hocmai

$$2\sin ^2x(4\sin ^4x-1)=\cos 2x(7\cos ^22x+3\cos 2x-1) \\
\leftrightarrow 2\sin ^2x(2\sin ^2x-1)(2\sin ^2x+1)=(1-2\sin ^2x)(7\cos ^22x+3\cos 2x-1) \\ \leftrightarrow 2\sin ^2x(2\sin ^2x-1)(2\sin ^2x+1)+(2\sin ^2x-1)(7\cos ^22x+3\cos 2x -1) \\ \leftrightarrow (2\sin ^2x-1)[2\sin ^2x(2\sin ^2x+1)+7\cos ^22x+3\cos 2x-1]=0 \\
\leftrightarrow -\cos 2x((1-\cos 2x)(2-\cos 2x)+7\cos ^22x+3\cos 2x-1)=0 $$
 
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