1)sin 2x =0,5 2)cos 2x =0,5 3)-3tgx=3 4)2ctgx=2

Question

1)sin 2x =0,5
2)cos 2x =0,5
3)-3tgx=3
4)2ctgx=2

Answer 1

1) sin2x=1/2
2x=(-1)arcsin1/2+Πn, n€Z
2x=(-1)^n Π/6+Πn, n€Z
x=(-1)^n Π/12+Πn/2, n€Z
2) cos2x=1/2
1-2sin^2x=1/2
2sin^2x=1/2
sin^2x=1/4
sinx=+-1/2
x1=(-1)^n arcsin1/2+Πn, n€Z
x2=Π-(-1)^n arcsin1/2+Πn, n€Z
3) -3tgx=3
tgx=-1
x=-Π/4+Πn, n€Z
4) 2ctgx=2
ctgx=1
x=Π/4+Πn, n€Z