Question

1)cos105-sin195+sin(-135)-cos135 2) tg18*tg288+sin32*sin148-sin302*sin122

Answer 1

1)
$cos(105^\circ)=cos(90^\circ+15^\circ)=-sin(15^\circ)\\ sin(195^\circ)=sin(180^\circ+15^\circ)=-sin(15^\circ)\\-sin(15^\circ)+sin(15^\circ)+sin(-135^\circ)-cos(135^\circ)=\\=-(sin(180^\circ-45^\circ)+cos(180^\circ-45^\circ))=-(sin(45^\circ)-cos(45^\circ))=0$

2)
$tg18^\circ*tg288^\circ+sin32^\circ*sin148^\circ-sin302^\circ*sin122^\circ\\\\sin148^\circ=sin(180^\circ-32^\circ)=sin32^\circ\\sin302^\circ=sin(270^\circ+32^\circ)=-cos32^\circ\\sin122^\circ=sin(90^\circ+32^\circ)=cos32^\circ\\\\sin^232^\circ+cos^232^\circ=1\\\\tg288^\circ=tg(270^\circ+18^\circ)=-ctg18^\circ\\\\tg18^\circ ctg18^\circ=1\\-1+1=0$