Đề trắc nghiệm ôn tập chương Công thức lượng giác Đại số 10 năm học 2018 - 2019

A. \(\cot 2x = \frac{{{{\cot }^2}x - 1}}{{2\cot x}}\)

B. \(\tan 2x = \frac{{2\tan x}}{{1 + {{\tan }^2}x}}\)

C. \(\cos 3x = 4{\cos ^3}x - 3\cos x\)

D. \(\sin 3x = 3\sin x - 4{\sin ^3}x\)

A. \(\cos \left( {a--b} \right) = \cos a.\cos b + \sin a.\sin b.\)

B. \(\cos \left( {a + b} \right) = \cos a.\cos b + \sin a.\sin b.\)

C. \(\sin \left( {a--b} \right) = \sin a.\cos b + \cos a.\sin b.\)

D. \(\sin \left( {a + b} \right) = \sin a.\cos b - \cos .\sin b.\)

A. \(\tan \left( {a - b} \right) = \frac{{\tan a + \tan b}}{{1 - \tan a\tan b}}.\)

B. \(\tan \left( {a--b} \right) = \tan a - \tan b.\)

C. \(\tan \left( {a + b} \right) = \frac{{\tan a + \tan b}}{{1 - \tan a\tan b}}.\)

D. \(\tan \left( {a + b} \right) = \tan a + \tan b.\)

A. \(\cos a\cos b = \frac{1}{2}\left[ {\cos \left( {a--b} \right) + \cos \left( {a + b} \right)} \right].\)

B. \(\sin a\sin b = \frac{1}{2}\left[ {\cos \left( {a--b} \right)--\cos \left( {a + b} \right)} \right].\)

C. \(\sin a\cos b = \frac{1}{2}\left[ {\sin \left( {a--b} \right) + \sin \left( {a + b} \right)} \right].\)

D. \(\sin a\cos b = \frac{1}{2}\left[ {\sin \left( {a - b} \right) - \cos \left( {a + b} \right)} \right].\)

A. \(\cos a + \cos b = 2\cos \frac{{a + b}}{2}.\cos \frac{{a - b}}{2}.\)

B. \(\cos a--\cos b = 2\sin \frac{{a + b}}{2}.\sin \frac{{a - b}}{2}.\)

C. \(\sin a + \sin b = 2\sin \frac{{a + b}}{2}.\cos \frac{{a - b}}{2}.\)

D. \(\sin a--\sin b = 2\cos \frac{{a + b}}{2}.\sin \frac{{a - b}}{2}.\)

A. \(\sin 2a.\)

B. \(\cos 2a.\)

C. \( - \frac{1}{2}.\)

D. \(  \frac{1}{2}.\)

A. \(\frac{{\sqrt 6  + \sqrt 2 }}{4}.\)

B. \(\frac{{\sqrt 6  - \sqrt 2 }}{4}.\)

C. \(-\frac{{\sqrt 6  + \sqrt 2 }}{4}.\)

D. \(\frac{{\sqrt 2  - \sqrt 6 }}{4}.\)

A. \(\frac{{\sqrt 3 }}{2}.\)

B. \(-\frac{{\sqrt 3 }}{2}.\)

C. \(\frac{{\sqrt 2 }}{2}.\)

D. \( - \frac{1}{2}.\)

A. \(\frac{{\sqrt 3 }}{2}.\)

B. \(-\frac{{\sqrt 3 }}{2}.\)

C. \(\frac{1}{2}.\)

D. \(-\frac{1}{2}.\)

A. 1

B. - 1

C. \(\frac{{\sqrt 3 }}{3}.\)

D. \(\sqrt 3 .\)

A. \(\frac{{\sqrt 2 }}{2},\frac{{\sqrt 3 }}{2}\)

B. \(\frac{{-\sqrt 2 }}{2},\frac{{\sqrt 3 }}{2}\)

C. \(\frac{{\sqrt 2 }}{2},-frac{{\sqrt 3 }}{2}\)

D. \(-\frac{{\sqrt 2 }}{2},-\frac{{\sqrt 3 }}{2}\)

A. \(\frac{1}{2}.\)

B. \(-\frac{1}{2}.\)

C. \(\frac{1}{4}.\)

D. \(-\frac{1}{4}.\)

A. \(2\left( {\sqrt 6  - \sqrt 3 } \right).\)

B. \(2\left( {\sqrt 6  + \sqrt 3 } \right).\)

C. \(2\left( {\sqrt 3  - \sqrt 2 } \right).\)

D. \(2\left( {\sqrt 3  + \sqrt 2 } \right).\)

A. 1

B. - 1

C. 2

D. - 2

A. \(\frac{1}{{16}}.\)

B. \(\frac{1}{{8}}.\)

C. \(\frac{3}{{16}}.\)

D. \(\frac{1}{{4}}.\)

A. \(\frac{1}{8}.\)

B. \(-\frac{1}{8}.\)

C. \(\frac{1}{4}.\)

D. \(-\frac{1}{4}.\)

A. \(\frac{2}{{\sqrt 3 }}.\)

B. \(\frac{4}{{\sqrt 3 }}.\)

C. \(\frac{6}{{\sqrt 3 }}.\)

D. \(\frac{8}{{\sqrt 3 }}.\)

A. 14

B. 16

C. 18

D. 10

A. \( - \frac{1}{2}.\)

B. \(  \frac{1}{2}.\)

C. \( - \frac{{\sqrt 3 }}{2}.\)

D. \( \frac{{\sqrt 3 }}{2}.\)

A. 1

B. - 1

C. 0

D. \(\frac{1}{2}.\)

A. \(\cos 50^\circ .\)

B. \(\cos 58^\circ .\)

C. \(\sin 50^\circ .\)

D. \(\sin 58^\circ .\)

A. 4

B. - 4

C. 8

D. - 8

A. \(\frac{\pi }{6}.\)

B. \(\frac{\pi }{5}.\)

C. \(\frac{\pi }{4}.\)

D. \(\frac{\pi }{3}.\)

A. \(\frac{\pi }{3}.\)

B. \(\frac{\pi }{4}.\)

C. \(\frac{\pi }{6}.\)

D. \(\frac{2\pi }{3}.\)

A. \(\frac{\pi }{4}.\)

B. \(\frac{3\pi }{4}.\)

C. \(\frac{\pi }{3}.\)

D. \(\pi\)

A. \(\frac{{11}}{{113}}.\)

B. \(\frac{{13}}{{113}}.\)

C. \(\frac{{15}}{{113}}.\)

D. \(\frac{{17}}{{113}}.\)

A. \(\frac{{2\sqrt 2  + 7\sqrt 3 }}{{18}}.\)

B. \(\frac{{3\sqrt 2  + 7\sqrt 3 }}{{18}}.\)

C. \(\frac{{4\sqrt 2  + 7\sqrt 3 }}{{18}}.\)

D. \(\frac{{5\sqrt 2  + 7\sqrt 3 }}{{18}}.\)

A. \(\frac{3}{4}.\)

B. \(\frac{4}{3}.\)

C. \(\frac{3}{2}.\)

D. \(\frac{2}{3}.\)

A. - 1

B. 1

C. - 2

D. 0

A. \(\frac{{\sin \left( {a + b} \right)}}{{\sin \left( {a - b} \right)}} = \frac{{\sin a + \sin b}}{{\sin a - \sin b}}.\)

B. \(\frac{{\sin \left( {a + b} \right)}}{{\sin \left( {a - b} \right)}} = \frac{{\sin a - \sin b}}{{\sin a + \sin b}}.\)

C. \(\frac{{\sin \left( {a + b} \right)}}{{\sin \left( {a - b} \right)}} = \frac{{\tan a + \tan b}}{{\tan a - \tan b}}.\)

D. \(\frac{{\sin \left( {a + b} \right)}}{{\sin \left( {a - b} \right)}} = \frac{{\cot a + \cot b}}{{\cot a - \cot b}}.\)

A. \(\sin \frac{{A + B + 3C}}{2} = \cos C.\)

B. \(\cos \left( {A + B--C} \right) = --\cos 2C.\)

C. \(\tan \frac{{A + B - 2C}}{2} = \cot \frac{{3C}}{2}.\)

D. \(\cot \frac{{A + B + 2C}}{2} = \tan \frac{C}{2}.\)

A. \(\cos \frac{{A + B}}{2} = \sin \frac{C}{2}.\)

B. \(\cos \left( {A + B + 2C} \right) = --\cos C.\)

C. \(\sin \left( {A + C} \right) = --\sin B.\)

D. \(\cos \left( {A + B} \right) = --\cos C.\)

A. \(\cos \frac{B}{2}\cos \frac{C}{2} - \sin \frac{B}{2}\sin \frac{C}{2} = \sin \frac{A}{2}.\)

B. \(\tan A + \tan B + \tan C = \tan A.\tan B.\tan C.\)

C. \(\cot A + \cot B + \cot C = \cot A.\cot B.\cot C.\)

D. \(\tan \frac{A}{2}.\tan \frac{B}{2} + \tan \frac{B}{2}.\tan \frac{C}{2} + \tan \frac{C}{2}.\tan \frac{A}{2} = 1.\)

A. \(\frac{{\sqrt 5 }}{3}.\)

B. \(\frac{5}{{\sqrt 3 }}.\)

C. \(\frac{{\sqrt 3 }}{5}.\)

D. \(\frac{3}{{\sqrt 5 }}.\)

A. \(\frac{{3\sin \alpha }}{{5 - 3\cos \alpha }}.\)

B. \(\frac{{3\sin \alpha }}{{5 + 3\cos \alpha }}.\)

C. \(\frac{{3\cos \alpha }}{{5 - 3\cos \alpha }}.\)

D. \(\frac{{3\cos \alpha }}{{5 + 3\cos \alpha }}.\)

A. \(\frac{{\cos \left( {4\alpha  + 30^\circ } \right)}}{{\cos \left( {4\alpha  - 30^\circ } \right)}}.\)

B. \(\frac{{\cos \left( {4\alpha  - 30^\circ } \right)}}{{\cos \left( {4\alpha  + 30^\circ } \right)}}.\)

C. \(\frac{{\sin \left( {4\alpha  + 30^\circ } \right)}}{{\sin \left( {4\alpha  - 30^\circ } \right)}}.\)

D. \(\frac{{\sin \left( {4\alpha  - 30^\circ } \right)}}{{\sin \left( {4\alpha  + 30^\circ } \right)}}.\)

A. \(\sin 33^\circ  + \cos 60^\circ  = \cos 3^\circ .\)

B. \(\frac{{\sin 9^\circ }}{{\sin 48^\circ }} = \frac{{\sin 12^\circ }}{{\sin 81^\circ }}.\)

C. \(\cos 20^\circ  + 2{\sin ^2}55^\circ  = 1 + \sqrt 2 \sin 65^\circ .\)

D. \(\frac{1}{{\cos 290^\circ }} + \frac{1}{{\sqrt 3 \sin 250^\circ }} = \frac{4}{{\sqrt 3 }}.\)

A. \(\tan \left( {\alpha  + \beta } \right) = 2\tan \beta .\)

B. \(\tan \left( {\alpha  + \beta } \right) = 3\tan \beta .\)

C. \(\tan \left( {\alpha  + \beta } \right) = 4\tan \beta .\)

D. \(\tan \left( {\alpha  + \beta } \right) =5\tan \beta .\)

A. \(\frac{3}{5}\left( {1 + \frac{{\sqrt 7 }}{4}} \right).\)

B. \(-\frac{3}{5}\left( {1 + \frac{{\sqrt 7 }}{4}} \right).\)

C. \(\frac{3}{5}\left( {1 - \frac{{\sqrt 7 }}{4}} \right).\)

D. \(-\frac{3}{5}\left( {1 - \frac{{\sqrt 7 }}{4}} \right).\)

A. \(\frac{{24\sqrt 3  - 7}}{{50}}.\)

B. \(\frac{{7 - 24\sqrt 3 }}{{50}}.\)

C. \(\frac{{22\sqrt 3  - 7}}{{50}}.\)

D. \(\frac{{7 - 22\sqrt 3 }}{{50}}.\)