\(sina+cosa=\frac{5}{4}\Rightarrow\left(sina+cosa\right)^2=\frac{25}{16}\)
\(\Rightarrow sin^2a+cos^2a+2sina.cosa=\frac{25}{16}\)
\(sina.cosa=\frac{\frac{25}{16}-1}{2}=\frac{9}{32}\)
b/ \(\left(sina-cosa\right)^2=sin^2a+cos^2a-2sinacosa\)
\(\left(sina-cosa\right)^2=1-2.\frac{9}{32}=\frac{7}{16}\)
\(\Rightarrow sina-cosa=\pm\frac{\sqrt{7}}{4}\)
c/ \(sin^3a-cos^3a=\left(sina-cosa\right)\left(sin^2a+cos^2a+sina.cosa\right)\)
\(=\left(sina-cosa\right)\left(1+\frac{9}{32}\right)=\pm\frac{41\sqrt{7}}{128}\)
Đúng 0
Bình luận (0)
