Sin 6x + sin 2X=0
! Решите

Пошаговое объяснение:

\ begin {gather} sin \ 2x + sin \ 6x = 0 \\ 2sin \ frac {2x + 6x} {2} cos \ frac {2x-6x} {2} = 0 \\ sin \ 4x \ cos \ 2x = 0 \\ \ left [{{sin \ 4x = O} \ atop {cos \ 2x = 0}} \ right. <=> \ left [{{4x = \ pi k} \ atop {2x = \ frac {\ pi} {2} +2 \ pi n}} \ right. <=> \ left [{{x = \ frac {\ pi k} {4} \ atop {x = \ frac {\ pi} {4} + \ pi n}} \ right. => x = \ dfrac {\ pi m} {4} \\ k \ in Z, \ n \ in Z, \ m \ in Z. \ ||| Ombem: \ \ \ dfrac {\ pi m} {4}; \ \ m \ in Z. \ end {gather}% 3D