Giải phương trình: \(\sin 3x - \sqrt 3 \cos 3x = 2\sin 2x.\)
A.\(x \in \left\{ {\frac{\pi }{3} + k2\pi ;\frac{{2\pi }}{{15}} + \frac{{k2\pi }}{5},k \in \mathbb{Z}} \right\}\)
B.\(x \in \left\{ {\frac{\pi }{3} + k2\pi ;\frac{{4\pi }}{{15}} + \frac{{k2\pi }}{5},k \in \mathbb{Z}} \right\}\)
C.\(x \in \left\{ {\frac{\pi }{3} + k\pi ;\frac{{2\pi }}{{15}} + \frac{{k\pi }}{5},k \in \mathbb{Z}} \right\}\)
D.\(x \in \left\{ {\frac{\pi }{3} + k\pi ;\frac{{4\pi }}{{15}} + \frac{{k\pi }}{5},k \in \mathbb{Z}} \right\}\)

Giải phương trình: \(\cos x - \sqrt 3 \sin x = 2\cos 3x.\)
A.\(x \in \left\{ {\frac{\pi }{6} - k\pi ;\frac{\pi }{{12}} + k\pi ;k \in \mathbb{Z}} \right\}\)
B.\(x \in \left\{ { - \frac{\pi }{6} - k\pi ;\frac{\pi }{{12}} + \frac{{k\pi }}{2};k \in \mathbb{Z}} \right\}\)
C.\(x \in \left\{ {\frac{\pi }{6} - k\pi ;\frac{\pi }{{12}} + \frac{{k\pi }}{2};k \in \mathbb{Z}} \right\}\)
D.\(x \in \left\{ { - \frac{\pi }{6} - k\pi ;\frac{\pi }{{12}} + k\pi ;k \in \mathbb{Z}} \right\}\)

Giải phương trình: \(\cos x - \sqrt 3 \sin x = 2\cos 3x\).
A.\(x \in \left\{ {\frac{\pi }{6} - k\pi ;\frac{\pi }{{12}} + k\pi ;k \in \mathbb{Z}} \right\}\)
B.\(x \in \left\{ {\frac{\pi }{6} - k\pi ; - \frac{\pi }{{12}} + k\pi ;k \in \mathbb{Z}} \right\}\)
C.\(x \in \left\{ {\frac{\pi }{6} - k\pi ; - \frac{\pi }{{12}} + \frac{{k\pi }}{2};k \in \mathbb{Z}} \right\}\)
D.\(x \in \left\{ {\frac{\pi }{6} - k\pi ;\frac{\pi }{{12}} + \frac{{k\pi }}{2};k \in \mathbb{Z}} \right\}\)

Giải phương trình: \(\tan x - 3\cot x = 4\left( {\sin x + \sqrt 3 \cos x} \right)\)
A.\(x \in \left\{ { - \frac{\pi }{3} + k\pi ;\frac{{4\pi }}{9} + \frac{{k2\pi }}{3};k \in \mathbb{Z}} \right\}\)
B.\(x \in \left\{ {\frac{\pi }{3} + k\pi ;\frac{{4\pi }}{9} + \frac{{k2\pi }}{3};k \in \mathbb{Z}} \right\}\)
C.\(x \in \left\{ { - \frac{\pi }{3} + k\pi ;\frac{{4\pi }}{9} + k2\pi ;k \in \mathbb{Z}} \right\}\)
D.\(x \in \left\{ {\frac{\pi }{3} + k\pi ;\frac{{4\pi }}{9} + k2\pi ;k \in \mathbb{Z}} \right\}\)

Giải phương trình: \(4\left( {{{\cos }^4}x + {{\sin }^4}x} \right) + \sqrt 3 \sin 4x = 2\)
A.\(\left[ \begin{array}{l}x = - \frac{\pi }{6} + \frac{{k\pi }}{2}\\x = \frac{\pi }{4} + \frac{{k\pi }}{2}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)
B.\(\left[ \begin{array}{l}x = - \frac{\pi }{6} + k\pi \\x = \frac{\pi }{4} + k\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)
C.\(\left[ \begin{array}{l}x = - \frac{\pi }{{12}} + k\pi \\x = \frac{\pi }{4} + k\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)
D.\(\left[ \begin{array}{l}x = - \frac{\pi }{{12}} + \frac{{k\pi }}{2}\\x = \frac{\pi }{4} + \frac{{k\pi }}{2}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)

Giải phương trình: \(\sin x\cos x + {\sin ^2}x = 1.\)
A.\(\left[ \begin{array}{l}x = \frac{\pi }{2} + k2\pi \\x = \frac{\pi }{4} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)
B.\(\left[ \begin{array}{l}x = \frac{\pi }{2} + k\pi \\x = \frac{\pi }{4} + k\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)
C.\(\left[ \begin{array}{l}x = - \frac{\pi }{2} + k\pi \\x = \frac{\pi }{4} + k\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)
D.\(\left[ \begin{array}{l}x = - \frac{\pi }{2} + k2\pi \\x = \frac{\pi }{4} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)

Rút gọn rồi tính giá trị biểu thức \(A\) khi \(x = \frac{7}{3}.\)
A.\(A = 1.\)
B.\(A = 2.\)
C.\(A = 3.\)
D.\(A = 4.\)

Tìm \(x\) biết \({x^2} - 4 - 2\left( {x + 2} \right) = 0.\)
A.\(x = 2\) hoặc \(x = 4.\)
B.\(x = - 2\) hoặc \(x = 4.\)
C.\(x = - 2\) hoặc \(x = - 4.\)
D.\(x = 2\) hoặc \(x = - 4.\)

Thực hiện các phép tính .
\(a)\,\,2{x^2}\left( {3{x^2} - 2x + 5} \right)\) \(b)\,\,\,\frac{x}{{{x^2} - 1}} - \frac{1}{{{x^2} - 1}}.\)
A.\(\begin{array}{l}a)\,\,6{x^4} - 4{x^3} + 10{x^2}\\b)\,\,\frac{1}{{x + 1}}\end{array}\)
B.\(\begin{array}{l}a)\,\,4{x^4} - 6{x^3} + 10{x^2}\\b)\,\,\frac{x}{{x - 1}}\end{array}\)
C.\(\begin{array}{l}a)\,\,4{x^4} - 6{x^3} + 5{x^2}\\b)\,\,\frac{1}{{x - 1}}\end{array}\)
D.\(\begin{array}{l}a)\,\,6{x^4} - 4{x^3} + 5{x^2}\\b)\,\,\frac{x}{{x + 1}}\end{array}\)

Giải phương trình: \(\sqrt 3 \left( {\cos 2x + \sin 3x} \right) = \sin 2x + \cos 3x.\)
A.\(\left[ \begin{array}{l}x = - \frac{\pi }{6} + k2\pi \\x = - \frac{\pi }{{10}} + \frac{{k2\pi }}{5}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)
B.\(\left[ \begin{array}{l}x = \frac{\pi }{6} + k2\pi \\x = \frac{\pi }{{10}} + \frac{{k2\pi }}{5}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)
C.\(\left[ \begin{array}{l}x = - \frac{\pi }{6} + k2\pi \\x = \frac{\pi }{{10}} + \frac{{k2\pi }}{5}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)
D.\(\left[ \begin{array}{l}x = \frac{\pi }{6} + k2\pi \\x = - \frac{\pi }{{10}} + \frac{{k2\pi }}{5}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)