Giúp mình 2 bài này với ạ vote đầy đủ

Đáp án:

\(\begin{array}{l}
2,\\
\left[ \begin{array}{l}
\cos x = \dfrac{{\sqrt {21} }}{5};\,\,\tan x = \dfrac{{2\sqrt {21} }}{{21}};\,\,\,\,\cot x = \dfrac{{\sqrt {21} }}{2}\\
\cos x =  - \dfrac{{\sqrt {21} }}{5};\,\,\tan x =  - \dfrac{{2\sqrt {21} }}{{21}};\,\,\,\,\cot x =  - \dfrac{{\sqrt {21} }}{2}
\end{array} \right.
\end{array}\)

\(\begin{array}{l}
3,\\
A = 4
\end{array}\)

Giải thích các bước giải:

 Bài 2:

Ta có:

\(\begin{array}{l}
{\sin ^2}x + {\cos ^2}x = 1\\
 \Leftrightarrow {\left( {\dfrac{2}{5}} \right)^2} + {\cos ^2}x = 1\\
 \Leftrightarrow \dfrac{4}{{25}} + {\cos ^2}x = 1\\
 \Leftrightarrow {\cos ^2}x = \dfrac{{21}}{{25}}\\
 \Rightarrow \left[ \begin{array}{l}
\cos x = \dfrac{{\sqrt {21} }}{5}\\
\cos x =  - \dfrac{{\sqrt {21} }}{5}
\end{array} \right.\\
TH1:\,\,\,\,\,\cos x = \dfrac{{\sqrt {21} }}{5}\\
 \Rightarrow \left\{ \begin{array}{l}
\tan x = \dfrac{{\sin x}}{{\cos x}} = \dfrac{2}{{\sqrt {21} }} = \dfrac{{2\sqrt {21} }}{{21}}\\
\cot x = \dfrac{{\cos x}}{{\sin x}} = \dfrac{{\sqrt {21} }}{2}
\end{array} \right.\\
TH2:\,\,\,\,\,\,\cos x =  - \dfrac{{\sqrt {21} }}{5}\\
 \Rightarrow \left\{ \begin{array}{l}
\tan x = \dfrac{{\sin x}}{{\cos x}} =  - \dfrac{2}{{\sqrt {21} }} =  - \dfrac{{2\sqrt {21} }}{{21}}\\
\cot x = \dfrac{{\cos x}}{{\sin x}} =  - \dfrac{{\sqrt {21} }}{2}
\end{array} \right.
\end{array}\)

Vậy \(\left[ \begin{array}{l}
\cos x = \dfrac{{\sqrt {21} }}{5};\,\,\tan x = \dfrac{{2\sqrt {21} }}{{21}};\,\,\,\,\cot x = \dfrac{{\sqrt {21} }}{2}\\
\cos x =  - \dfrac{{\sqrt {21} }}{5};\,\,\tan x =  - \dfrac{{2\sqrt {21} }}{{21}};\,\,\,\,\cot x =  - \dfrac{{\sqrt {21} }}{2}
\end{array} \right.\)

Bài 3:

\(\begin{array}{l}
\sin x = \cos \left( {90^\circ  - x} \right)\\
{\sin ^2}x + {\cos ^2}x = 1\\
A = {\sin ^2}10^\circ  + {\sin ^2}20^\circ  + {\sin ^2}30^\circ  + {\sin ^2}40^\circ  + {\sin ^2}50^\circ  + {\sin ^2}60^\circ  + {\sin ^2}70^\circ  + {\sin ^2}80^\circ \\
 = {\sin ^2}10^\circ  + {\sin ^2}20^\circ  + {\sin ^2}30^\circ  + {\sin ^2}40^\circ  + {\cos ^2}\left( {90^\circ  - 50^\circ } \right) + {\cos ^2}\left( {90^\circ  - 60^\circ } \right) + {\cos ^2}\left( {90^\circ  - 70^\circ } \right) + {\cos ^2}\left( {90^\circ  - 80^\circ } \right)\\
 = {\sin ^2}10^\circ  + {\sin ^2}20^\circ  + {\sin ^2}30^\circ  + {\sin ^2}40^\circ  + {\cos ^2}40^\circ  + {\cos ^2}30^\circ  + {\cos ^2}20^\circ  + {\cos ^2}10^\circ \\
 = \left( {{{\sin }^2}10^\circ  + {{\cos }^2}10^\circ } \right) + \left( {{{\sin }^2}20^\circ  + {{\cos }^2}20^\circ } \right) + \left( {{{\sin }^2}30^\circ  + {{\cos }^2}30^\circ } \right) + \left( {{{\sin }^2}40^\circ  + {{\cos }^2}40^\circ } \right)\\
 = 1 + 1 + 1 + 1\\
 = 4
\end{array}\)