Đáp án: $\sin \widehat A = \dfrac{{\sqrt {10} }}{{10}};\cos \widehat A = \dfrac{{3\sqrt {10} }}{{10}};\cot \widehat A = 3$
Giải thích các bước giải:
$\begin{array}{l}
0 < \widehat A < {90^0}\\
\Leftrightarrow \left\{ \begin{array}{l}
0 < \sin \widehat A < 1\\
0 < \cos \widehat A < 1
\end{array} \right.\\
\cot \widehat A = \dfrac{1}{{\tan \widehat A}} = 3\\
Do:\dfrac{1}{{{{\cos }^2}\widehat A}} = {\tan ^2}\widehat A + 1 = \dfrac{1}{{{3^2}}} + 1 = \dfrac{{10}}{9}\\
\Leftrightarrow {\cos ^2}\widehat A = \dfrac{9}{{10}}\\
\Leftrightarrow \cos \widehat A = \dfrac{{3\sqrt {10} }}{{10}}\\
\tan \widehat A = \dfrac{{\sin \widehat A}}{{\cos \widehat A}}\\
\Leftrightarrow \sin \widehat A = \tan \widehat A.\cos \widehat A = \dfrac{{3\sqrt {10} }}{{10}}.\dfrac{1}{3} = \dfrac{{\sqrt {10} }}{{10}}\\
Vậy\,\sin \widehat A = \dfrac{{\sqrt {10} }}{{10}};\cos \widehat A = \dfrac{{3\sqrt {10} }}{{10}};\cot \widehat A = 3
\end{array}$
