Question

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

Answer 1

$sin825cdot cos(-15)+cos75cdot sin(-555)-tg75cdot tg165=\\=sin(2cdot 360+105)cdot cos15+cos(90-15)cdot (-sin(360+195))-\\-tg(90-15)cdot tg(180-15)=\\=sin(90+15)cdot cos15-sin15cdot sin (180+15)-ctg15cdot tg(-15)=\\=cos15cdot cos15-sin15cdot (-sin15)-ctg15cdot (-tg15)=\\=(cos^215+sin^215)+ctg15cdot tg15=1+1=2\\\P.S.quad sin^2 alpha +cos^2 alpha =1; ; ;; ; tg alpha cdot ctg=1$