Đề kiểm tra Bài tập cuối chương III (có lời giải) - Đề 1

Chọn A

Ta có: \(P = \sin 30^\circ \cos 60^\circ  + sin60^\circ cos30^\circ  = \frac{1}{2}.\frac{1}{2} + \frac{{\sqrt 3 }}{2}.\frac{{\sqrt 3 }}{2} = 1\).

Chọn A

Ta có \(\sin {0^{\rm{o}}} + \cos {0^{\rm{o}}} = 1\).

Chọn A

\(E = \sin {36^{\rm{o}}}\cos {6^{\rm{o}}}\sin \left( {{{90}^{\rm{o}}} + {{36}^{\rm{o}}}} \right)\cos \left( {{{90}^{\rm{o}}} - {6^{\rm{o}}}} \right) = \sin {36^{\rm{o}}}\cos {6^{\rm{o}}} - \cos {36^{\rm{o}}}\sin {6^{\rm{o}}} = \sin {30^{\rm{o}}} = \frac{1}{2}\)

Chọn C

\(S = {\sin ^2}{2^{\rm{o}}} + {\sin ^2}{4^{\rm{o}}} + {\sin ^2}{6^{\rm{o}}} + ... + {\sin ^2}{84^{\rm{o}}} + {\sin ^2}{86^{\rm{o}}} + {\sin ^2}{88^{\rm{o}}}\)

\[ = \left( {{{\sin }^2}{2^{\rm{o}}} + {{\sin }^2}{{88}^{\rm{o}}}} \right) + \left( {{{\sin }^2}{4^{\rm{o}}} + {{\sin }^2}{{86}^{\rm{o}}}} \right) + ... + \left( {{{\sin }^2}{{44}^{\rm{o}}} + {{\sin }^2}{{46}^{\rm{o}}}} \right)\]

\( = \left( {{{\sin }^2}{2^{\rm{o}}} + {{\cos }^2}{2^{\rm{o}}}} \right) + \left( {{{\sin }^2}{4^{\rm{o}}} + {{\cos }^2}{4^{\rm{o}}}} \right) + ... + \left( {{{\sin }^2}{{44}^{\rm{o}}} + {{\cos }^2}{{44}^{\rm{o}}}} \right) = 22\).

Chọn B

\(\tan \alpha  - \cot \alpha  = 3 \Leftrightarrow {\left( {\tan \alpha  - \cot \alpha } \right)^2} = 9 \Leftrightarrow {\tan ^2}\alpha  + {\cot ^2}\alpha  - 2\tan \alpha .\cot \alpha  = 9\)

\( \Leftrightarrow {\tan ^2}\alpha  + {\cot ^2}\alpha  - 2 = 9 \Leftrightarrow {\tan ^2}\alpha  + {\cot ^2}\alpha  = 11\).

Chọn B

\({\tan ^2}x{\sin ^2}x - {\tan ^2}x + {\sin ^2}x = {\tan ^2}x\left( {{{\sin }^2}x - 1} \right) + {\sin ^2}x = \frac{{{{\sin }^2}x}}{{{{\cos }^2}x}}\left( { - {{\cos }^2}x} \right) + {\sin ^2}x = 0\).

Chọn B

Ta có \(\cos \alpha  =  - \cos \left( {180^\circ  - \alpha } \right)\quad \left( {0^\circ  \le \alpha  \le 180^\circ } \right)\)nên suy ra \(\cos \alpha  + \cos \left( {180^\circ  - \alpha } \right) = 0\).

Do đó: \[A = \left( {\cos 20^\circ  + \cos 160^\circ } \right) + \left( {\cos 40^\circ  + \cos 140^\circ } \right) + \left( {\cos 60^\circ  + \cos 120^\circ } \right)\]\[ + \left( {\cos 80^\circ  + \cos 100^\circ } \right) + \cos 180^\circ \] \( = \,\,\cos 180^\circ  =  - 1\).

Chọn A

\(f\left( x \right) = {\cos ^2}x\left( {{{\cos }^2}x + {{\sin }^2}x} \right) + {\sin ^2}x = {\cos ^2}x + {\sin ^2}x = 1\).