Cho cot a=3/4 tính sin a cos a

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
\cot a = \dfrac{3}{4} \Leftrightarrow \dfrac{{\cos a}}{{\sin a}} = \dfrac{3}{4} \Leftrightarrow \cos a = \dfrac{3}{4}\sin a\\
{\sin ^2}a + {\cos ^2}a = 1\\
 \Leftrightarrow {\sin ^2}a + {\left( {\dfrac{3}{4}\sin a} \right)^2} = 1\\
 \Leftrightarrow {\sin ^2}a + \dfrac{9}{{16}}{\sin ^2}a = 1\\
 \Leftrightarrow \dfrac{{25}}{{16}}{\sin ^2}a = 1\\
 \Leftrightarrow {\sin ^2}a = \dfrac{{16}}{{25}}\\
 \Rightarrow \left[ \begin{array}{l}
\sin a = \dfrac{4}{5} \Rightarrow \cos a = \dfrac{3}{4}\sin a = \dfrac{3}{4}.\dfrac{4}{5} = \dfrac{3}{5}\\
\sin a =  - \dfrac{4}{5} \Rightarrow \cos a = \dfrac{3}{4}.\sin a = \dfrac{3}{4}.\left( { - \dfrac{4}{5}} \right) =  - \dfrac{3}{5}
\end{array} \right.
\end{array}\)