2sin((π/4)-(13x/2))·cos((π/4+(7x/2))=0 -2sin((13x/2)-(π/4))·cos((π/4+(7x/2))=0 sin((13x/2)-(π/4))=0 или cos((π/4+(7x/2))=0 (13x/2)-(π/4)=πk, k∈Z или (7x/2)+(π/4)=(π/2)+πn, n∈Z
(13x/2)=(π/4)+πk, k∈Z или (7x/2)=-(π/4)+(π/2)+πn, n∈Z x=(π/26)+(2π/13)·k, k∈Z или x)=(π/14)+(2π/7)·n, n∈Z
Answers & Comments
Verified answer
Cos3x=sin((π/2)-3x)sin((π/2)-3x)=sin10x;
sin((π/2)-3x)-sin10x=0.
Формула
sinα-sinβ=2sin((α-β)/2)·cos((α+β)/2)
2sin((π/4)-(13x/2))·cos((π/4+(7x/2))=0
-2sin((13x/2)-(π/4))·cos((π/4+(7x/2))=0
sin((13x/2)-(π/4))=0 или cos((π/4+(7x/2))=0
(13x/2)-(π/4)=πk, k∈Z или (7x/2)+(π/4)=(π/2)+πn, n∈Z
(13x/2)=(π/4)+πk, k∈Z или (7x/2)=-(π/4)+(π/2)+πn, n∈Z
x=(π/26)+(2π/13)·k, k∈Z или x)=(π/14)+(2π/7)·n, n∈Z