Phương trình lượng giác.:confused::confused:

L

lan_phuong_000

Đây là những dạng bài rất cơ bản nha bạn! :)
1. $sin(\dfrac{\pi}{4} + 4)=sin(2x - \dfrac{\pi}{4})$
\Leftrightarrow $\left[\begin{matrix}\dfrac{\pi}{4} + 4=2x - \dfrac{\pi}{4} + k2\pi\\ \dfrac{\pi}{4} + 4= \pi - 2x + \dfrac{\pi}{4} \end{matrix}\right.$

\Leftrightarrow $\left[\begin{matrix}x= \dfrac{\pi}{2} + k2\pi\\ x=\dfrac{\pi}{3} + k.\dfrac{2\pi}{3} \end{matrix}\right.$

2. $sinx.(sin2x -1)=0$ (giải như giải pt tích)
\Leftrightarrow $\left[\begin{matrix}sinx=0\\ sin2x =1 \end{matrix}\right.$

\Leftrightarrow $\left[\begin{matrix}x= k\pi\\ 2x = \dfrac{\pi}{2} + k2\pi \end{matrix}\right.$

\Leftrightarrow $\left[\begin{matrix}x= k\pi\\ x = \dfrac{\pi}{4} + k\pi \end{matrix}\right.$

3. $sin(x - 120) - cos2x = 0$ (sd ct $cosx=sin(90 - x)$)
\Leftrightarrow $sin(x - 120) = sin(90 - 2x}$

\Leftrightarrow $\left[\begin{matrix}x - 120 = 90 - 2x + k.360 \\ x - 120 = 180 - 90 + 2x + k.360 \end{matrix}\right.$

\Leftrightarrow $\left[\begin{matrix}x = 70 + k.120\\ x = -210 - k.360\end{matrix}\right.$

4. $sin(x + \dfrac{2\pi}{3}) = cos3x$ (tương tự bài 3)
\Leftrightarrow $sin(x + \dfrac{2\pi}{3}) = sin(\dfrac{\pi}{2} - 3x)$

\Leftrightarrow $\left[\begin{matrix} x + \dfrac{2\pi}{3} = \dfrac{\pi}{2} - 3x + k2\pi \\ x + \dfrac{2\pi}{3}= \pi - \dfrac{\pi}{2} + 3x + k2\pi \end{matrix}\right.$

\Leftrightarrow $\left[\begin{matrix}x= \dfrac{-\pi}{24} + k.\dfrac{\pi}{2}\\ x= \dfrac{\pi}{12} - k.\dfrac{\pi}{2} \end{matrix}\right.$



 
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