Cho tan a = $\frac{3}{5}$. Tính giá trị biểu thức: a) M = $\frac{sina.cosa}{sin^2a-cos^2a}$ b) P = $\frac{sin^3a+cos^3a}{2sina.cos^2a+cosa.sin^2a}$

Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
\tan a = \dfrac{3}{5} \Leftrightarrow \dfrac{{\sin a}}{{\cos a}} = \dfrac{3}{5} \Leftrightarrow \sin a = \dfrac{3}{5}\cos a\\
a,\\
M = \dfrac{{\sin a.\cos a}}{{{{\sin }^2}a – {{\cos }^2}a}} = \dfrac{{\dfrac{3}{5}\cos a.\cos a}}{{{{\left( {\dfrac{3}{5}\cos a} \right)}^2} – {{\cos }^2}a}} = \dfrac{{\dfrac{3}{5}{{\cos }^2}a}}{{\dfrac{9}{{25}}{{\cos }^2}a – {{\cos }^2}a}} = \dfrac{{\dfrac{3}{5}{{\cos }^2}a}}{{ – \dfrac{{16}}{{25}}{{\cos }^2}a}} =  – \dfrac{{15}}{{16}}\\
b,\\
P = \dfrac{{{{\sin }^3}a + {{\cos }^3}a}}{{2\sin a.{{\cos }^2}a + \cos a.{{\sin }^2}a}} = \dfrac{{{{\left( {\dfrac{3}{5}\cos a} \right)}^3} + {{\cos }^3}a}}{{2.\left( {\dfrac{3}{5}\cos a} \right).{{\cos }^2}a + \cos a.{{\left( {\dfrac{3}{5}\cos a} \right)}^2}}} = \dfrac{{\dfrac{{27}}{{125}}{{\cos }^3}a + {{\cos }^3}a}}{{\dfrac{6}{5}{{\cos }^3}a + \dfrac{9}{{25}}{{\cos }^3}a}} = \dfrac{{\dfrac{{152}}{{125}}{{\cos }^3}a}}{{\dfrac{{39}}{{25}}{{\cos }^2}a}} = \dfrac{{152}}{{195}}
\end{array}\)