Question

4. [ 3 б] Упростите выражение:
ПОЖАЛУЙСТА 4 ЗАДАНИЕ

Answer 1

Відповідь:

4 cos (α)

Пояснення:

($\frac{sin(\alpha )}{1+cos(\alpha )} +\frac{sin(\alpha )}{1-cos(\alpha )}$)*sin(2$\alpha$)=$\frac{sin(\alpha )(1-cos(\alpha ))+sin(\alpha )(1+cos(\alpha ))}{(1-cos(\alpha) )(1+cos(\alpha ))} *sin(2\alpha )$=$\frac{sin(\alpha )(1-cos(\alpha )+1+cos(\alpha ))}{1-cos^{2}(\alpha ) } *sin(2\alpha )$=$\frac{sin(\alpha )*2}{sin^{2}(\alpha ) } *sin(2\alpha )$=$\frac{2}{sin(\alpha )}*sin(2\alpha )$=$\frac{2*2*sin(\alpha )*cos(\alpha )}{sin(\alpha) }$=$\frac{4*sin(\alpha )*cos(\alpha )}{sin(\alpha )}$=4 cos(α)

sin(2α)=2*sin(α)*cos(α)