Đáp án:
b. \(\dfrac{{2\sqrt 2 }}{9}\)
Giải thích các bước giải:
\(\begin{array}{l}
a.{\sin ^2}a + {\cos ^2}a = 1\\
\to \dfrac{4}{9} + {\cos ^2}a = 1\\
\to {\cos ^2}a = \dfrac{5}{9}\\
\to {\tan ^2}a = \dfrac{{{{\sin }^2}a}}{{{{\cos }^2}a}} = \dfrac{4}{9}:\dfrac{5}{9} = \dfrac{4}{5}\\
{\cot ^2}a = \dfrac{{{{\cos }^2}a}}{{{{\sin }^2}a}} = \dfrac{5}{4}\\
\to P = {\tan ^2}a - 2{\cot ^2}a = \dfrac{4}{5} - 2.\dfrac{5}{4} = - \dfrac{{17}}{{10}}\\
b.M = \dfrac{1}{{\dfrac{{\sin a}}{{\cos a}} + \dfrac{{\cos a}}{{\sin a}}}}\\
= \dfrac{1}{{\dfrac{{{{\sin }^2}a + {{\cos }^2}a}}{{\sin a.\cos a}}}}\\
= 1:\dfrac{1}{{\sin a.\cos a}} = \sin a.\cos a = \dfrac{{2\sqrt 2 }}{9}
\end{array}\)
