Sin825*cos(-15)+cos75*sin(-555)-tg75*tg165=2 докажите тождество

[latex]sin825\cdot cos(-15)+cos75\cdot sin(-555)-tg75\cdot tg165=\\\\=sin(2\cdot 360+105)\cdot cos15+cos(90-15)\cdot (-sin(360+195))-\\\\-tg(90-15)\cdot tg(180-15)=\\\\=sin(90+15)\cdot cos15-sin15\cdot sin (180+15)-ctg15\cdot tg(-15)=\\\\=cos15\cdot cos15-sin15\cdot (-sin15)-ctg15\cdot (-tg15)=\\\\=(cos^215+sin^215)+ctg15\cdot tg15=1+1=2\\\\\\P.S.\quad sin^2 \alpha +cos^2 \alpha =1\; \; ;\; \; tg \alpha \cdot ctg=1[/latex]