Question

sin4a-sin5a-sin6a+sin7a=-4sina/2*sina*sin11a/2

Answer 1

sin4a + sin7a -( sin5a+sin6a) = -4sina/2*sina*sin11a/2

2sin (11a/2)cos(3a/2) - 2sin (11a/2)cos(a/2)=-4sina/2*sina*sin11a/2

2sin(11a/2) *( cos(3a/2)-cos(a/2)+2*sina/2*sina)=0

2sin(11a/2) *( cos(3a/2)-cos(a/2)+cos(a/2)-cos(3a/2))=0

sin ( 11a/2)=0 

11a/2=pi*k

a=2/11*pi*k где k- целые числа