Question

sin(6x-п/3)=sin(2x+п/4)

Answer 1

https://znanija.com/task/34713605

sin(6x - π/3)=sin(2x + π/4)

Ответ:  7π/4 +(π/2)*n  n  ∈ ℤ .      π/6 +(π/4)* k  ,   k  ∈ ℤ.

Объяснение:

sin(6x - π/3) = sin(2x + π/4)

(6x - π/3) - (2x+ π/4)   = 2πn      ⇒ x = 7π/4 +(π/2)*n ,       n  ∈ ℤ.

(6x - π/3) + (2x+ π/4)  =  π+ 2πk ⇒ x = π/6 +(π/4)* k  ,   k  ∈ ℤ.

P.S.   * * * * * * * * * * * * * * * * * * * * * * * * * * *

sinα=sinβ  ⇔sinα- sinβ =0 ⇔2(sin(α- β)/2) )* ( cos(α+ β)/2) )=0.

sin(α - β)/2 =0 ⇒ (α- β)/2 = π*n ⇔ α- β = 2π*n ;    

cos(α+ β)/2 =0  ⇒(α + β)/2 = π/2 +π*k⇔ α + β =π +2π*k .       ||  (2k+1)π ||