Trang chủ Đề thi & kiểm tra Lớp 12 Toán học BTVN - Phương trình lượng giác (Tiết 2) - Có lời giải chi tiết

BTVN - Phương trình lượng giác (Tiết 2) - Có lời g...

  • Câu 1 : Giải phương trình: \(\sqrt 3 \sin 2x + \cos 2x = 1\)

    A \(S = \left\{ {k\pi ;\frac{\pi }{2} + k2\pi } \right\}\)

    B \(S = \left\{ {k\pi ;\frac{\pi }{4} + k2\pi } \right\}\)

    C \(S = \left\{ {k\pi ;\frac{\pi }{3} + k\pi } \right\}\)

    D \(S = \left\{ {k2\pi ;\frac{\pi }{4} + k2\pi } \right\}\)

  • Câu 2 : Giải phương trình: \(\cos 3x - \sin 3x = \sqrt 2 \) với \(x \in \left( { - \frac{\pi }{2};\pi } \right)\)

    A \(S = \left\{ { - \frac{\pi }{{12}};\frac{{5\pi }}{{12}}} \right\}\)

    B \(S = \left\{ { - \frac{\pi }{{12}};\frac{{7\pi }}{{12}}} \right\}\)

    C \(S = \left\{ {\frac{\pi }{{12}}; - \frac{{7\pi }}{{12}}} \right\}\)

    D \(S = \left\{ {\frac{\pi }{{12}}; - \frac{{5\pi }}{{12}}} \right\}\)

  • Câu 3 : Giải phương trình: \(\sin x + \sqrt 3 \cos x = 1.\)

    A \(S = \left\{ { - \frac{\pi }{6} + k2\pi ;\frac{\pi }{2} + k2\pi } \right\}\)

    B \(S = \left\{ {\frac{\pi }{6} + k2\pi ; - \frac{\pi }{2} + k2\pi } \right\}\)

    C \(S = \left\{ { - \frac{\pi }{6} + k2\pi ;\frac{\pi }{3} + k2\pi } \right\}\)

    D \(S = \left\{ {\frac{\pi }{6} + k2\pi ; - \frac{\pi }{3} + k2\pi } \right\}\)

  • Câu 4 : Giải phương trình: \(\sqrt 3 \cos x - \sin x = \sqrt 2 .\)

    A \(S = \left\{ {\frac{\pi }{{12}} + k2\pi ; - \frac{{5\pi }}{{12}} + k2\pi } \right\}\)

    B \(S = \left\{ { - \frac{\pi }{{12}} + k2\pi ;\frac{{5\pi }}{{12}} + k2\pi } \right\}\)

    C \(S = \left\{ { - \frac{\pi }{{12}} + k2\pi ; - \frac{{5\pi }}{{12}} + k2\pi } \right\}\)

    D \(S = \left\{ {\frac{\pi }{{12}} + k2\pi ;\frac{{5\pi }}{{12}} + k2\pi } \right\}\)

  • Câu 5 : Giải phương trình: \(5\cos x + 12\sin x - 13 = 0\).

    A \(x \in \left\{ {\arccos \frac{8}{{13}} + k2\pi ,k \in \mathbb{Z}} \right\}\)

    B \(x \in \left\{ {\arccos \frac{5}{9} + k2\pi ,k \in \mathbb{Z}} \right\}\)

    C \(x \in \left\{ {\arccos \frac{8}{9} + k2\pi ,k \in \mathbb{Z}} \right\}\)

    D \(x \in \left\{ {\arccos \frac{5}{{13}} + k2\pi ,k \in \mathbb{Z}} \right\}\)

  • Câu 6 : 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 \(x \in \left\{ {\frac{\pi }{3} + k\pi ;\frac{{4\pi }}{{15}} + \frac{{k\pi }}{5},k \in \mathbb{Z}} \right\}\)

  • Câu 7 : Giải phương trình: \(\sqrt 3 \sin 2x + \sin \left( {\frac{\pi }{2} + 2x} \right) = 2\sin x\).

    A \(x \in \left\{ {\frac{\pi }{6} + k2\pi ;\frac{{5\pi }}{{18}} + \frac{{k2\pi }}{3},k \in \mathbb{Z}} \right\}\)

    B \(x \in \left\{ { - \frac{\pi }{6} + k2\pi ;\frac{{5\pi }}{{18}} + k2\pi ,k \in \mathbb{Z}} \right\}\)

    C \(x \in \left\{ { - \frac{\pi }{6} + k2\pi ;\frac{{5\pi }}{{18}} + \frac{{k2\pi }}{3},k \in \mathbb{Z}} \right\}\)

    D \(x \in \left\{ {\frac{\pi }{6} + k2\pi ;\frac{{5\pi }}{{18}} + k2\pi ,k \in \mathbb{Z}} \right\}\)

  • Câu 8 : 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 \(x \in \left\{ {\frac{\pi }{6} - k\pi ;\frac{\pi }{{12}} + \frac{{k\pi }}{2};k \in \mathbb{Z}} \right\}\)

  • Câu 9 : Giải phương trình: \(\sin 9x + \sqrt 3 \cos 7x = \sin 7x + \sqrt 3 \cos 9x\)

    A \(x \in \left\{ {k\pi ; - \frac{\pi }{{48}} + \frac{{k\pi }}{8};k \in \mathbb{Z}} \right\}\)

    B \(x \in \left\{ {k\pi ; - \frac{\pi }{{24}} + \frac{{k\pi }}{4};k \in \mathbb{Z}} \right\}\)

    C \(x \in \left\{ {\frac{{k\pi }}{2}; - \frac{\pi }{{48}} + \frac{{k\pi }}{8};k \in \mathbb{Z}} \right\}\)

    D \(x \in \left\{ {\frac{{k\pi }}{2}; - \frac{\pi }{{24}} + \frac{{k\pi }}{4};k \in \mathbb{Z}} \right\}\)

  • Câu 10 : Giải phương trình: \(\tan x - 3\cot x = 4\left( {\sin x + \sqrt 3 \cos x} \right)\)

    A \(x \in \left\{ { - \frac{\pi }{3} + k2\pi ;\frac{{4\pi }}{9} + \frac{{k2\pi }}{3};k \in \mathbb{Z}} \right\}\)

    B \(x \in \left\{ {\frac{\pi }{3} + k2\pi ;\frac{{4\pi }}{9} + \frac{{k2\pi }}{3};k \in \mathbb{Z}} \right\}\)

    C \(x \in \left\{ { - \frac{\pi }{3} + k2\pi ;\frac{{4\pi }}{9} + k2\pi ;k \in \mathbb{Z}} \right\}\)

    D \(x \in \left\{ {\frac{\pi }{3} + k2\pi ;\frac{{4\pi }}{9} + k2\pi ;k \in \mathbb{Z}} \right\}\)

  • Câu 11 : 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 \(\left[ \begin{array}{l}x =  - \frac{\pi }{{12}} + \frac{{k\pi }}{2}\\x = \frac{\pi }{4} + \frac{{k\pi }}{2}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)

  • Câu 12 : Giải phương trình: \(3\sin 3x - \sqrt 3 \cos 9x = 1 + 4{\sin ^3}3x\)

    A \(\left[ \begin{array}{l}x = \frac{\pi }{9} + \frac{{k2\pi }}{9}\\x = \frac{{7\pi }}{{36}} + \frac{{k2\pi }}{9}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)

    B \(\left[ \begin{array}{l}x = \frac{\pi }{9} + \frac{{k2\pi }}{9}\\x = \frac{{7\pi }}{{54}} + \frac{{k2\pi }}{9}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)

    C \(\left[ \begin{array}{l}x = \frac{\pi }{{18}} + \frac{{k2\pi }}{9}\\x = \frac{{7\pi }}{{54}} + \frac{{k2\pi }}{9}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)

    D \(\left[ \begin{array}{l}x = \frac{\pi }{{18}} + \frac{{k2\pi }}{9}\\x = \frac{{7\pi }}{{36}} + \frac{{k2\pi }}{9}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)

  • Câu 13 : 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 \(\left[ \begin{array}{l}x =  - \frac{\pi }{2} + k2\pi \\x = \frac{\pi }{4} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\)

  • Câu 14 : Giải phương trình \(8\cos x = \frac{{\sqrt 3 }}{{\sin x}} + \frac{1}{{\cos x}}\).   

    A \(\left[ \begin{array}{l}x =  - \frac{{11\pi }}{{12}} + k\pi \\x = \frac{{ - 5\pi }}{{12}} + k\pi \\x = \frac{{ - 2\pi }}{3} + k\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\,\)

    B \(\left[ \begin{array}{l}x = \frac{{11\pi }}{{12}} + k\pi \\x = \frac{{5\pi }}{{12}} + k\pi \\x = \frac{{ - 2\pi }}{3} + k\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\,\)

    C \(\left[ \begin{array}{l}x =  - \frac{{11\pi }}{{12}} + k\pi \\x = \frac{{5\pi }}{{12}} + k\pi \\x = \frac{{2\pi }}{3} + k\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\,\)

    D \(\left[ \begin{array}{l}x = \frac{{11\pi }}{{12}} + k\pi \\x = \frac{{ - 5\pi }}{{12}} + k\pi \\x = \frac{{2\pi }}{3} + k\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\,\)

  • Câu 15 : Giải phương trình: \(\sin x + \sqrt 3 \cos x = 2\sin \left( {x + \frac{\pi }{6}} \right).\)

    A \(x = \frac{\pi }{4} + k2\pi \,\,\,\left( {k \in \mathbb{Z}} \right)\)

    B \(x = \frac{\pi }{2} + k\pi \,\,\,\left( {k \in \mathbb{Z}} \right)\)

    C \(x = \frac{\pi }{2} + k2\pi \,\,\,\left( {k \in \mathbb{Z}} \right)\)

    D \(x = \frac{\pi }{4} + k\pi \,\,\,\left( {k \in \mathbb{Z}} \right)\)

  • Câu 16 : Giải phương trình: \(\cos 2x - \sqrt 3 \sin 2x = \sqrt 3 \sin x + \cos x.\)

    A \(x = \frac{{k\pi }}{3}\,\,\left( {k \in \mathbb{Z}} \right)\)

    B \(x =  - \frac{{2\pi }}{3} + k2\pi \)

    C \(x =  - \frac{{k\pi }}{3}\,\,\left( {k \in \mathbb{Z}} \right)\)

    D \(x = \frac{{k2\pi }}{3}\,\,\left( {k \in \mathbb{Z}} \right)\)

  • Câu 17 : 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 \(\left[ \begin{array}{l}x = \frac{\pi }{6} + k2\pi \\x =  - \frac{\pi }{{10}} + \frac{{k2\pi }}{5}\end{array} \right.\,\,\,\left( {k \in \mathbb{Z}} \right)\)

Đáp án có ở chi tiết câu hỏi nhé!!! (click chuột vào câu hỏi).

Lớp 12 Toán học Lớp 12 - Toán học
Xem thêm