Question

помогите решить два примера.(номер 18.26)

Answer 1

a)|sin(x/2)|=√3|cos(x/2)|

|tg(x/2)|=1/√3

|x/2|=pi/3 и |x/2|= 2pi/3

|x|=2pi/3+2pik и |x|=4pi/3+2pik

x={-2pi/3+2pik;2pi/3+2pik;4pi/3+2pik;-4pi/3+2pik}

б)|sin4x|=|cos4x|

|tg4x|]=1; 4x=pi/4+pi/2; x=pi/16+pi/8

Answer 2

sin²(x/2)=3*(cos²(x/2))

Для упрощения, пусть х/2=t ⇒

sin²t=3*cos²t

sin²t=3-3*sin²t

4*sin²t=3 |÷4

sin²t=3/4

sint=√(3/4)

sint=+/-√3/2

t₁=π/3 ⇒ x/2=π/3+2πn x₁=2π/3+2πn

t₂=2π/3 ⇒ x/2=2π/3+2πn x₂=4π/3+2πn

t₃=4π/3 ⇒ x/2=4π/3+2πn x₃=8π/3+2

t₄=5π/3 ⇒ x/2=5π/3+2πn x₄=10π/3+2πn