`A=sin45^o .cos45^o +cos60^o .sin30^o -cos30^o .sin60^o`

`=(sin45^o .cos45^o )+(cos60^o .sin30^o) -(cos30^o .sin60^o )`

`=((\sqrt{2})/(2).(\sqrt{2})/(2))+(1/2. 1/2)-((\sqrt{3})/(2).(\sqrt{3})/(2))`

`=1/2 +1/4 -3/4`

`=0`