Question

Зная,что sin a + cos a=1/2 ,найти sin a cos a

Answer 1

$\mathtt{sin\alpha+cos\alpha=\frac{1}{2};~(sin\alpha+cos\alpha)^2=(\frac{1}{2})^2;~}\\\mathtt{sin^2\alpha+2sin\alpha cos\alpha+cos^2\alpha=1+2sin\alpha cos\alpha=\frac{1}{4};~}\\\mathtt{sin\alpha cos\alpha=\frac{\frac{1}{4}-1}{2}=\frac{-\frac{3}{4}}{2}=-\frac{3}{8}}$