1) √3/2sin3x-1/2cos3x=-1 2) sin^2 x-2sin2x-5cos^2 x=0 3) 1-cosx=sin x/2

Question

1) √3/2sin3x-1/2cos3x=-1

2) sin^2 x-2sin2x-5cos^2 x=0

3) 1-cosx=sin x/2

Answer 1

1) √3/2sin3x-1/2cos3x=-1
sin(3x-pi/6)= -1
3x-pi/6 = -pi/2+2pi*k
3x=-pi/3+2pi*k
x= -pi/9 + 2pi*k /3

2) sin^2 x-2sin2x-5cos^2 x=0 Делим на cos^2x
tg^2x-4tgx-5=0
D=16+20=36
tgx=5 ->x=arctgx5+pi*k
tgx= -1 ->x= -pi/4+pi*n