Question

Cho \(sinx+cosx=\frac{1}{2}\). Tinh gtri \(sin^3x+cos^3x\)

Answer 1

\(\left(sinx+cosx\right)^2=\frac{1}{4}\Rightarrow1+2sinx.cosx=\frac{1}{4}\Rightarrow sinx.cosx=-\frac{3}{8}\)

\(sin^3x+cos^3x=\left(sinx+cosx\right)^3-3sinxcosx\left(sinx+cosx\right)\)

\(=\left(\frac{1}{2}\right)^3-3.\left(-\frac{3}{8}\right).\frac{1}{2}=...\)