Cho biết \(0 var DOMAIN = "https://hoc247.net/"; var STATI...

* Hướng dẫn giải

Ta có

\(\begin{array}{l} P = {\sin ^4}\alpha + {\cos ^4}\alpha = {\left( {{{\sin }^2}\alpha } \right)^2} + {\left( {{{\cos }^2}\alpha } \right)^2}\\ = {\left( {{{\sin }^2}\alpha } \right)^2} + 2{\sin ^2}\alpha .{\cos ^2}\alpha + {\left( {{{\cos }^2}\alpha } \right)^2} - 2{\sin ^2}\alpha .{\cos ^2}\alpha \\ = {\left( {{{\sin }^2}\alpha + {{\cos }^2}\alpha } \right)^2} - 2{\sin ^2}\alpha .{\cos ^2}\alpha \\ = {1^2} - 2.{\left( {\sin \alpha .\cos \alpha } \right)^2}\\ = 1 - 2.\frac{1}{4} = \frac{1}{2} \end{array}\)