Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
P = {\sin ^4}\left( {\dfrac{\pi }{2} - x} \right) - {\cos ^4}\left( {\dfrac{\pi }{2} - x} \right) - 2{\cos ^2}\left( {\pi + x} \right) + 1\\
= {\cos ^4}x - {\sin ^4}x - 2.{\cos ^2}\left[ {\pi - \left( {\pi + x} \right)} \right] + 1\\
= \left( {{{\cos }^2}x - {{\sin }^2}x} \right)\left( {{{\cos }^2}x + {{\sin }^2}x} \right) - 2{\cos ^2}x + 1\\
= {\cos ^2}x - {\sin ^2}x - 2{\cos ^2}x + 1\\
= 1 - \left( {{{\sin }^2}x + {{\cos }^2}x} \right)\\
= 1 - 1 = 0\\
2,\\
\tan a.\cot a = \dfrac{{\sin a}}{{\cos a}}.\dfrac{{\cos a}}{{\sin a}} = 1\\
P = \left| {\tan a + \cot a} \right|\\
\Leftrightarrow {P^2} = {\tan ^2}a + 2.\tan .\cot a + {\cot ^2}a\\
\Leftrightarrow {P^2} = {\left( {\tan a - \cot a} \right)^2} + 4\tan a.\cot a\\
\Leftrightarrow {P^2} = {\left( {2\sqrt 3 } \right)^2} + 4.1\\
\Leftrightarrow {P^2} = 16\\
\Leftrightarrow P = 4
\end{array}\)
