sin120°+cos750°+sin(-690°)cos(-660°)+tan675°+cot765°-tan1020
来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/05/09 14:04:37
sin120°+cos750°+sin(-690°)cos(-660°)+tan675°+cot765°-tan1020°+cot(-1230°)等于?
sin120°=cos30°
cos750°=cos30°
sin(-690°)=sin30°
cos(-660°)=cos60°
tan675°=tan45°
cot765°=cot45°
tan1020°=-tan60°
cot(-1230°)=cot30°
sin120°+cos750°+sin(-690°)cos(-660°)+tan675°+cot765°-tan1020°+cot(-1230°)
=cos30°+cos30°+sin30°cos60°+tan45°+cot45°+tan60°+cot30°
=2cos30°+sin30°sin30°+2+2tan60°
=√3+1/4+2+2√3
=3√3+9/4
cos750°=cos30°
sin(-690°)=sin30°
cos(-660°)=cos60°
tan675°=tan45°
cot765°=cot45°
tan1020°=-tan60°
cot(-1230°)=cot30°
sin120°+cos750°+sin(-690°)cos(-660°)+tan675°+cot765°-tan1020°+cot(-1230°)
=cos30°+cos30°+sin30°cos60°+tan45°+cot45°+tan60°+cot30°
=2cos30°+sin30°sin30°+2+2tan60°
=√3+1/4+2+2√3
=3√3+9/4
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