Question

1)1+ctg4x=0
2)2sin x/2=3sin² x/2

Answer 1

1) ctg(4x) = -1
4x = 3π/4 + πk
x = 3π/16 + πk/4
2) 3sin^2(x/2) - 2sin(x/2) = 0
sin(x/2) * (3sin(x/2) - 2) = 0
a) sin(x/2) = 0, (x/2) = πk, x = 2πk
b) sin(x/2) = 2/3, (x/2) = (-1)^k * (arcsin(2/3)) + 2πk