Use sumdifference identities at some point sintheta omega s

Use sum/difference identities at some point sin(theta - omega) sin(theta + omega) = sin^2(theta) - sin^2(omega)

Solution

sin( + ) = sin cos + cos sin

sin( ) = sin cos cos sin

sin( + )sin( )=(sin cos + cos sin )(sin cos cos sin )

=sin^2 cos ^2 -cos^2 sin ^2

we know cos^2=1 - sin^2

so,

=sin^2 (1 - sin^2) - (1 - sin^2) sin ^2

=sin^2-sin^2 as other parts get cancelled

hence proved