Question

Se senx-cosx=1/2, calcule o valor de senx.cosx

Answer 1

Vejamos:

$\left(sen(x)-cos(x)\right)^2=\left(\frac{1}{2}\right)^2 \\ \\ \left(sen(x)-cos(x)\right)^2=\left(\frac{1}{4}\right) \\ \\ sen^2(x)+cos^2(x)-2sen(x)cos(x)=1-2sen(x)cos(x)=\frac{1}{4} \\ \\ 2sen(x)cos(x)=\frac{3}{4} \\ \\ sen(x)cos(x)=\frac{\frac{3}{4}}{2} \\ \\ sen(x)cos(x)=\frac{3}{8}$