Sin ^2 a (5p\4 - 2a ) -sin ^2a (5p\4+2a )

Question

Sin ^2 a (5p\4 - 2a ) -sin ^2a (5p\4+2a )

Answer 1

Sin²(5π/4-2a)-sin²(5π/4+2a)=(sin(5π/4-2a)-sin(5π/4+2a))(sin(5π/4-2a)+sin(5π/4+2a))=
=2sin(-2a)cos5π/4*sin5π/4cos(-2a)=-sin4a*(-cosπ/4)*(-sinπ/4)=
=-sin4a*(-√2/2)*(-√2/2)=-1/2*sin4a