Question

a)sin43cos13-sin47cos77
б)sin34cos11+sin56cos79

в) $frac{cos3 alpha }{sin alpha } + frac{sin3 alpha }{cos alpha }$
г) $tg alpha +ctg alpha$
д) $cos frac{ pi }{7} cos frac{2 pi }{7} cos frac{4 pi }{7}$

Answer 1

sin43cos13-sin(90-43)cos(90-13)=sin43cos13-cos43sin13=sin(43-13)=sin30=1/2
sin34cos11+sin(90-34)cos(90-11)=sin34cos11+cos34sin11=sin(34+11)=sqrt(2)/2
(sinacos3a+sin3acosa)/sinacosa=sin4a/1/2sin2a=2sin4a/sin2a=4cos2a
sina/cosa+cosa/sina=1/sinacosa=2/sin2a
sinП/7cosП/7cos2П/7cos4П/7/sinП/7=1/8sin8П/7/sinп/7=1/8(sin(П+П/7)/sinП/7)=-1/8