Question

[Phạm Thị Huyền Trang huyentrang]

1.Giải các phương trình sau :

a) 2sinx+1=0

b) √2 cosx+1=0

c) tanx-√3=0

d) cotx=0

2. Giải các phương trình sau :

a) sin²x+sinx-2=0

b) cot²x-2cotx-3=0

3.Giải các phương trình sau :

sin²x+sin²2x+sin²3x=3/2

Answer 1

[Nguyễn Việt Lâm]

1/ \(sinx=-\frac{1}{2}=sin\left(-\frac{\pi}{6}\right)\)

\(\Rightarrow\left[{}\begin{matrix}x=-\frac{\pi}{6}+k2\pi\\x=\frac{7\pi}{6}+k2\pi\end{matrix}\right.\)

b/ \(cos=-\frac{\sqrt{2}}{2}=cos\left(\frac{3\pi}{4}\right)\)

\(\Rightarrow x=\pm\frac{3\pi}{4}+k2\pi\)

c/ \(tanx=\sqrt{3}=tan\left(\frac{\pi}{3}\right)\)

\(\Rightarrow x=\frac{\pi}{3}+k\pi\)

d/ \(cotx=0\Rightarrow x=\frac{\pi}{2}+k\pi\)

Answer 2

[Nguyễn Việt Lâm]

2/

a/ \(sin^2x+sinx-2=0\)

\(\Leftrightarrow\left(sinx-1\right)\left(sinx+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx=1\\sinx=-2\left(vn\right)\end{matrix}\right.\) \(\Rightarrow x=\frac{\pi}{2}+k2\pi\)

b/ \(cot^2x-2cotx-3=0\)

\(\Leftrightarrow\left(cotx+1\right)\left(cotx-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cotx=-1\\cotx=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-\frac{\pi}{4}+k\pi\\x=arccot3+k\pi\end{matrix}\right.\)

3/ \(\Leftrightarrow1-cos2x+1-cos4x+1-cos6x=3\)

\(\Leftrightarrow cos2x+cos6x+cos4x=0\)

\(\Leftrightarrow2coss4x.cos2x+cos4x=0\)

\(\Leftrightarrow cos4x\left(2cos2x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cos4x=0\\cos2x=-\frac{1}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}4x=\frac{\pi}{2}+k\pi\\2x=\frac{2\pi}{3}+k2\pi\\2x=-\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{8}+\frac{k\pi}{4}\\x=\frac{\pi}{3}+k\pi\\x=-\frac{\pi}{3}+k\pi\end{matrix}\right.\)