Sin5a-sin6a-sin7a+sin8a

Question

Sin5a-sin6a-sin7a+sin8a

Answer 1

(sin5a-sin7a)+(sin8a-sin6a)=2sin(-a)*cos6a+2sina*cos7a=
=-2sinacos6a+2sinacos7a=2sina*(cos7a-cos6a)=2sina*(-2sina/2*sin13a/2)=
=-4sina/2*sina*sin13a/2