Question

упростите выражение

Answer 1

$dfrac{1}{mathrm{tg}(x)}+dfrac{sin(x)}{1+cos(x)}=dfrac{cos(x)}{sin(x)}+dfrac{sin(x)}{1+cos(x)}=dfrac{cos(x)left(1+cos(x)right)+sin^2(x)}{sin(x)left(1+cos(x)right)}=medskip\=dfrac{cos(x)+cos^2(x)+sin^2(x)}{sin(x)left(1+cos(x)right)}=dfrac{left(cos(x)+1right)}{sin(x)left(1+cos(x)right)}=dfrac{1}{sin(x)}=mathrm{cosec}(x)$