Question

sin160°cos110°+sin250°cos340°+tg110°tg340°​

Answer 1

Ответ:

-1 - 2/sin40°

Объяснение:

sin160°·cos110°+sin250°·cos340°+tg110°+tg340°=

=sin(180°-20°)·cos(90°+20°)+sin(270°-20°)·cos(360°-20°)+

+tg(90°+20°)+tg(360°-20°)=

=sin20°·(-sin20°)+(-cos20°)·cos20°-ctg20°-tg20°=

= -sin²20°-cos²20°-(cos20°/sin20°)-(sin20°/cos20°)=

= -(sin²20°+cos²20°)-( (cos²20°+sin²20°)/(sin20°·cos20°))=

= -1 - 1/(sin20°·cos20°)= -1-2/(2·sin20°·cos20°)=

= -1 - 2/sin(2·20°)= -1 - 2/sin40°