Question

ПОМОГИТЕ!!Упростите выражения

Answer 1

$1)tg(-\alpha)*Cos\alpha+Sin\alpha=-\frac{Sin\alpha }{Cos\alpha }*Cos\alpha+Sin\alpha=-Sin\alpha+Sin\alpha=0\\\\2)\frac{Ctg(-\alpha)*Sin\alpha}{Cos\alpha}=\frac{-\frac{Cos\alpha }{Sin\alpha}*Sin\alpha }{Cos\alpha }=\frac{-Cos\alpha }{Cos\alpha}=-1$

$3)Cos^{2}\alpha*tg^{2}(-\alpha)-1=Cos^{2}\alpha *\frac{Sin^{2}\alpha}{Cos^{2}\alpha  }-1=Sin^{2}\alpha-1=-Cos^{2}\alpha$

$4)\frac{1-tg(-\alpha)}{Sin\alpha+Cos(-\alpha)} =\frac{1+\frac{Sin\alpha }{Cos\alpha}}{Sin\alpha+Cos\alpha}=\frac{Sin\alpha+Cos\alpha}{Cos\alpha*(Sin\alpha+Cos\alpha)}=\frac{1}{Cos\alpha }$