6sin(2x-pi/3)cos(3x+pi/3)-3sin(5x+pi/6) выражение - вопрос №623333565223820 от zhanym2 22.05.2023 21:41

Question

Алгебра: 6sin(2x-pi/3)cos(3x+pi/3)-3sin(5x+pi/6) выражение

zhanym2 · Answer

6*1/2(sin(2x-π/3-3x-π/3)+sin(2x-π/3+3x+π/3))-3sin5xcosπ/6-3cos5xsinπ/6=
3sin(-x-2π/3)+3sin5x-1,5sin5x-1,5cos5x=-3sin(x+2π/3)+1,5sin5x-1,5cos5x=
-3sinxcos2π/3-3cosxsin2π/3+1,5sin5x-1,5cos5x=1,5sinx-3√3/2cosx+
+1,5sin5x-1,5cosx=1,5(sinx+sin5x)-3√3/2cosx-1,5cos5x=3sin2xcos6x--3√3/2cosx-1,5cos5x