Думаю как-то так
sin2004°cos1974°- sin1974°cos2004°=1/2(sin(2004-1974)-sin(2004+1974)-1/2(sin(1974-2004)+sin(1974+2004))=0.5(sin30+sin3978)-0.5(sin(-30)+sin3978)=
=0.5sin30+0.5sin3978+0.5sin30-0.5sin3978=1/2(sin30+sin30)=(1/2)*2sin30=sin30=1/2
