Lời giải

sin⁴ a + cos⁴ a = (sin² a + cos² a)² – 2sin² a cos² a = 1 – 2 . (sin a cos a)²

= \(1 - 2.{\left( {\frac{{\sin 2a}}{2}} \right)^2} = 1 - \frac{1}{2}{\sin ^2}2a\)\( = 1 - \frac{1}{2}.\frac{2} = 1 - \frac{4} = \frac{3}{4} + \frac{1}{4}\cos 4a\).

Vậy \({\sin ^4}a + {\cos ^4}a = 1 - \frac{1}{2}{\sin ^2}2a = \frac{3}{4} + \frac{1}{4}\cos 4a\).