Question

100 баллов. Упростите выражения​

Answer 1

$1)-Sin(2x-\frac{\pi }{2})+Sin(2x+\pi)*Ctgx=Sin(\frac{\pi }{2}-2x)+Sin(\pi+2x)*Ctgx=Cos2x-Sin2x*Ctgx=Cos2x-\frac{2Sinx Cosx*Cosx}{Sinx}=Cos2x-2Cos^{2}x=2Cos^{2}x-1-2Cos^{2}x=-1$

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