Make mme understand that circcled part..only;for experts..pl no links
when multiplied by sin 3A you will get :-
1/4{3 sin A sin 3A - sin2 3A + cos2 3A + 3 cos A cos 3A }
rewrite it as :-
1/4{ (3 sin A sin 3A + 3 cos A cos 3A) + cos2 3A- sin2 3A}
1/4{ 3 (sin A sin 3A + cos A cos 3A) + cos2 3A- sin2 3A}
by applying formulae of cos (A-B) and cos 2A
{cos (3A-A) = sin A sin 3A- cos A cos 3A and also cos2 3A - sin2 3A = cos 2(3A) }
we get,
1/4{3 (cos (3A-A)) + cos 3 (2A)}
1/4(3 cos 2A + (4 cos3 2A - 3 cos 2A))
1/4 (3 cos 2A + 4 cos3 2A - 3 cos 2A)
1/4 (4 cos3 2A) = cos3 2A
1/4{3 sin A sin 3A - sin2 3A + cos2 3A + 3 cos A cos 3A }
rewrite it as :-
1/4{ (3 sin A sin 3A + 3 cos A cos 3A) + cos2 3A- sin2 3A}
1/4{ 3 (sin A sin 3A + cos A cos 3A) + cos2 3A- sin2 3A}
by applying formulae of cos (A-B) and cos 2A
{cos (3A-A) = sin A sin 3A- cos A cos 3A and also cos2 3A - sin2 3A = cos 2(3A) }
we get,
1/4{3 (cos (3A-A)) + cos 3 (2A)}
1/4(3 cos 2A + (4 cos3 2A - 3 cos 2A))
1/4 (3 cos 2A + 4 cos3 2A - 3 cos 2A)
1/4 (4 cos3 2A) = cos3 2A