Question

A) sin(2п-α)+cos(4п-α)tg(α+7п)= b) ctg x> -√3 c) 2cos²x-5cos x+2=0 d) 1-2cos²δ /cos δ-sin δ=

Answer 1

$sin(2 \pi - \alpha )+cos(4 \pi - \alpha )tg(7 \pi + \alpha )= - sin \alpha +cos \alpha *tg \alpha =$$- sin \alpha +cos \alpha * \frac{sin \alpha }{cos \alpha } =- sin \alpha +sin \alpha =0$

2) $\pi k\ \textless \ x\ \textless \ \frac{7 \pi }{6} + \pi k,$ k∈Z
3) введем замену cosx=t  /t/≤1
$2t^2-5t+2=0$
D=25-16=9
t1=2 не подходит
t2=1/2
$cosx= \frac{1}{2}$
x=±$\frac{ \pi }{3} +2 \pi k,$,k∈Z

4) $\frac{cos^2 \alpha +sin^2 \alpha -2cos^2 \alpha }{cos \alpha -sin \alpha } = \frac{sin^2 \alpha -cos^2 \alpha }{cos \alpha -sin \alpha } = -(sin \alpha +cos \alpha )$

Answer 2

1)-sina+cosa*sina/cosa=-sina+sina=0
2)x∈(πn;7π/6+πn)
3)cosx=a
2a²-5a+2=0
D=25-16=9
a1=(5-3)/4=1/2⇒cosx=1/2⇒x=+-π/3+2πn
a2=(5+3)/4=2⇒cosx=2>1 нет решения
4)(cos²δ+sin²δ-2cos²δ)/(cosδ-sinδ)=(sinδ-cosδ)(sinδ+cosδ)/(cosδ-sinδ)=
=-sinδ-cosδ