Question

Тригонометрия a)tg(x-pi\6)=1 б)sin2x-4sinxcosx-5cos2x=0 в)sin2x+sinx cosx=0

Answer 1

a)tg(x-pi\6)=1
x-pi/6=pi/4+pik
x=pi/4+pi/6+pik
x=5pi/2+pik
б)sin2x-4sinxcosx-5cos2x=0
sin2x-2sin2x-5cos2x=0
sin2x=-5cos2x
tg2x=-5
2x=arctg(-5)+pik
x=(1/2)arctg(-5)+pik/2

в)sin2x+sinx cosx=0
sin2x+(1/2)sin2x=0
(3/2)sin2x=0
sin2x=0
2x=pik
x=pik/2