Question

30 баллов, соч по алгебре​

Answer 1

Ответ:

$cos15^\circ +cos30^\circ +cos45^\circ +...+cos150^\circ +cos165^\circ =\\\\\\=\Big[\ \underline {15}+15=\underline {30}\ ,\ 30+15=\underline {45}\ ,\ 45+15=\underline {60}\ ,\ 60+15=\underline{75}\ ,\\\\75+15=\underline {90}\ ,\ 90+15=\underline {105}\ ,\ 105+15=\underline {120}\ ,\ 120+15=\underline {135}\ ,\\\\135+15=\underline {150}\ ,\ 150+15=\underline {165}\ \Big]=\\\\\\=(cos15^\circ +cos165^\circ )+(cos30^\circ +cos150^\circ )+(cos45^\circ +cos135^\circ )+$

$+(cos60^\circ +cos120^\circ )+(cos75^\circ +cos105^\circ )+cos90^\circ =\\\\=2\, \underbrace {cos90^\circ }_{0}\cdot cos75^\circ +2\, \underbrace{cos90^\circ }_{0}\cdot cos60^\circ +2\, \underbrace {cos90^\circ }_{0}\cdot cos45^\circ +\\\\+2\, \underbrace {cos90^\circ }_{0}\cdot cos30^\circ +2\, \underbrace {cos90^\circ }_{0}\cdot cos15^\circ +\underbrace {cos90^\circ }_{0}=0$