BTVN - Phương trình lượng giác (Tiết 4) - Có lời g...

  • Câu 1 : \(4\sqrt 3 \sin x\cos x + 4{\cos ^2}x = 2{\sin ^2}x + \frac{5}{2}.\)

    A \(\left[ \begin{array}{l}x = \frac{\pi }{3} + k\pi \\x = \arctan \left( {\frac{{ - \sqrt 3 }}{9}} \right) + k\pi \end{array} \right.\left( {k \in Z} \right)\)

    B \(\left[ \begin{array}{l}x =  - \frac{\pi }{3} + k\pi \\x = \arctan \left( {\frac{{\sqrt 3 }}{9}} \right) + k\pi \end{array} \right.\left( {k \in Z} \right)\)

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

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

  • Câu 2 : \(25{\sin ^2}x + 15\sin 2x + 9{\cos ^2}x = 25.\)

    A \(x = \frac{\pi }{2} + k\pi \), \(x = \arctan \frac{7}{{15}} + k\pi \left( {k \in Z} \right)\)

    B \(x = \frac{\pi }{2} + k\pi \), \(x = \arctan \frac{3}{5} + k\pi \left( {k \in Z} \right)\)

    C \(x = \frac{\pi }{2} + k\pi \), \(x = \arctan \frac{8}{{15}} + k\pi \left( {k \in Z} \right)\)

    D \(x = \frac{\pi }{2} + k\pi \), \(x = \arctan \frac{2}{5} + k\pi \left( {k \in Z} \right)\)

  • Câu 3 : \(2{\sin ^2}x + 3\sqrt 3 \sin x\cos x - {\cos ^2}x = 2.\)

    A \(x = \frac{\pi }{6} + k2\pi \left( {k \in Z} \right)\)

    B \(x = \frac{\pi }{6} + k\pi \left( {k \in Z} \right)\)

    C \(x =  - \frac{\pi }{6} + k\pi \left( {k \in Z} \right)\)

    D \(x =  - \frac{\pi }{6} + k2\pi \left( {k \in Z} \right)\)

  • Câu 4 : \(2{\sin ^2}x - \sin x\cos x - {\cos ^2}x = 2.\)

    A \(x = \arctan 3 + k\pi \)

    B \(x = \arctan \left( { - 3} \right) + k2\pi \)

    C \(x = \arctan \left( { - 3} \right) + k\pi \)

    D \(x = \arctan 3 + k2\pi \)

  • Câu 5 : \(4{\sin ^3} + 3\sqrt 2 \sin 2x = 8\sin x.\)

    A \(x = k\pi \), \(x =  \pm \frac{\pi }{4} + k2\pi \)

    B \(x = k\pi \), \(x =  \pm \frac{\pi }{4} + k\pi \)

    C \(x = k\pi \), \(x =  \pm \frac{\pi }{2} + k\pi \)

    D \(x = k\pi \), \(x =  \pm \frac{\pi }{2} + k2\pi \)

  • Câu 6 : \({\sin ^3}x - \sqrt 3 {\cos ^3}x = \sin x{\cos ^2}x - \sqrt 3 {\sin ^2}x\cos x.\)

    A \(\left[ \begin{array}{l}x = \frac{\pi }{4} + k\pi \\x =  - \frac{\pi }{3} + k\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)

    B \(\left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x =  - \frac{\pi }{3} + k2\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)

    C \(\left[ \begin{array}{l}x =  \pm \frac{\pi }{4} + k2\pi \\x =  - \frac{\pi }{3} + k2\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)

    D \(\left[ \begin{array}{l}x =  \pm \frac{\pi }{4} + k\pi \\x =  - \frac{\pi }{3} + k\pi \end{array} \right.\,\,\,\,\left( {k \in \mathbb{Z}} \right)\)