Question

упростите ввражение: ​

Answer 1

Ответ:

решение на фотографии

Answer 2

$1)\frac{Sin\alpha Cos\alpha}{tg\alpha }-1=\frac{Sin\alpha Cos\alpha}{\frac{Sin\alpha }{Cos\alpha}}-1=\frac{Sin\alpha Cos^{2}\alpha}{Sin\alpha}-1=Cos^{2}\alpha-1=\boxed{-Sin^{2}\alpha} \\\\\\2)\frac{Sin\alpha Cos\alpha}{Ctg\alpha}-1=\frac{Sin\alpha Cos\alpha}{\frac{Cos\alpha }{Sin\alpha} }-1=\frac{Sin^{2}\alpha Cos\alpha}{Cos\alpha}-1=Sin^{2}\alpha-1=\boxed{-Cos^{2} \alpha}$

$3)\frac{1}{1-Cos\alpha}-\frac{1}{1+Cos\alpha}=\frac{1+Cos\alpha-1+Cos\alpha}{(1-Cos\alpha)(1+Cos\alpha)}=\frac{2Cos\alpha }{1-Cos^{2}\alpha}= \boxed{\frac{2Cos\alpha }{Sin^{2}\alpha}}\\\\\\4)\frac{1+tg\alpha }{1+Ctg\alpha }=\frac{1+tg\alpha }{1+\frac{1}{tg\alpha}} =\frac{(1+tg\alpha)*tg\alpha}{tg\alpha+1 }= \boxed{tg\alpha}$