Cho sin α + cos α = $\frac{1}{3}$ với $- \frac{\pi }{2} < \alpha < 0$. Tính:

C = sin³ α + cos³ α;

Ta có:

C = sin³ α + cos³ α = (sin α + cos α)³ – 3 sin α cos α(sin α + cos α)

$= {\left( {\frac{1}{3}} \right)^3} - 3.\left( { - \frac{4}{9}} \right).\left( {\frac{1}{3}} \right) = \frac{{13}}{{27}}$.