Verified answer

Формула синуса суммы:

sinα·cosβ+cosαsinβ=sin(α+β)

Уравнение:

sinx(2x+x)=(√2)/2

sin3x=(√2)/2

3x=(-1)ⁿarcsin((√2)/2)+π·n, n∈Z

3x=(-1)ⁿ(π/4)+π·n, n∈Z,

x=(-1)ⁿ(π/12)+(π/3)·n, n∈Z

О т в е т.

a)

-1)ⁿ(π/12)+(π/3)·n, n∈Z

б)

(π/4);(2π/3); (3π/4);

При  

n=0

x=(π/12)∉[π/6;π]

При

n=1

-(π/12)+(π/3)·1=3π/12=(π/4)∈[π/6;π]

При

n=2

(π/12)+(π/3)·2=9π/12=(3π/4)∈[π/6;π]

При

n=3

-(π/12)+(π/3)·3=8π/12=(2π/3)∈[π/6;π]