Question

Докажите тождество cos(4α)-sin(4α)*ctg(2α)=-1

Answer 1

$Cos4 \alpha -Sin4 \alpha *Ctg2 \alpha =Cos4 \alpha -2Sin2 \alpha Cos2 \alpha * \frac{Cos2 \alpha }{Sin2 \alpha }=$$Cos4 \alpha-2Cos ^{2}2 \alpha =2Cos ^{2}2 \alpha -1 -2Cos ^{2}2 \alpha =-1\\\\-1=-1$
Тождество доказано

Answer 2

2сos²2a-1-2sin2acos2a*cos2a/sin2a=2сos²2a-1-2cos²2a=-1
-1=-1