Question

Bài 1: Giải phương trình: 3cos4x - sin²2x + cos2x - 2 = 0

Bài 2: Giải phương trình: \(\frac{1}{sin^2x}\)+ 3cotx + 1 = 0

Bài 3: Giải phương trình: \(\sqrt{3}\) tanx + cotx - \(\sqrt{3}\) - 1 = 0

Bài 4: Giải phương trình: cos2x - 3cosx = 4cos²\(\frac{x}{2}\)

Answer 1

1.

\(\Leftrightarrow3\left(2cos^22x-1\right)-\left(1-cos^22x\right)+cos2x-2=0\)

\(\Leftrightarrow7cos^22x+cos2x-6=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cos2x=-1\\cos2x=\frac{6}{7}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{2}+k\pi\\x=\pm\frac{1}{2}arccos\left(\frac{6}{7}\right)+k\pi\end{matrix}\right.\)

2.

ĐKXĐ: ...

\(\Leftrightarrow1+cot^2x+3cotx+1=0\)

\(\Leftrightarrow cot^2x+3cotx+2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cotx=-1\\cotx=-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\frac{\pi}{4}+k\pi\\x=arccot\left(-2\right)+k\pi\end{matrix}\right.\)

Answer 2

3.

ĐKXĐ; ..

\(\sqrt{3}tanx+\frac{1}{tanx}-\sqrt{3}-1=0\)

\(\Leftrightarrow\sqrt{3}tan^2x-\left(\sqrt{3}+1\right)tanx+1=0\)

\(\Leftrightarrow\left[{}\begin{matrix}tanx=1\\tanx=\frac{1}{\sqrt{3}}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+k\pi\\x=\frac{\pi}{6}+k\pi\end{matrix}\right.\)

4.

\(\Leftrightarrow2cos^2x-1-3cosx=2+2cosx\)

\(\Leftrightarrow2cos^2x-5cosx-3=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cosx=-\frac{1}{2}\\cosx=3>1\left(l\right)\end{matrix}\right.\)

\(\Rightarrow x=\pm\frac{2\pi}{3}+k2\pi\)