Đáp án:
B
Giải thích các bước giải:
\(\begin{array}{l}
\sin \alpha - \cos \alpha = \frac{1}{{\sqrt 5 }}\\
\leftrightarrow {\sin ^2}\alpha + {\cos ^2}\alpha - 2\sin \alpha .\cos \alpha = \frac{1}{5}\\
\leftrightarrow 1 - 2\sin \alpha .\cos \alpha = \frac{1}{5}\\
\leftrightarrow \sin \alpha .\cos \alpha = \frac{2}{5}
\end{array}\)
Có \({\sin ^4}\alpha + {\cos ^4}\alpha = {({\sin ^2}\alpha + {\cos ^2}\alpha )^2} - 2si{n^2}\alpha .{\cos ^2}\alpha = 1 - 2si{n^2}\alpha .{\cos ^2}\alpha = 1 - 2.{\left( {\frac{2}{5}} \right)^2} = \frac{{17}}{{25}}\)
\( \to P = \sqrt {\frac{{17}}{{25}}} = \frac{{\sqrt {17} }}{5}\)
