Question

cos40*sin 70*cos 80 вычислить без таблиц

Answer 1

cos40*sin70*cos80 =

cos40*sin70 = (1/2)*(sin(70-40)+sin(70+40))= (1/2)*(sin30+ sin(90+20))=

=(1/2)*(1/2  +cos20) =1/4+(1/2)cos20

 cos40*sin70*cos80 = (1/4+(1/2)cos20)*cos80 = (1/4)cos80 +(1/2)*(1/2)(cos(80-20)+cos(80+20)) = (1/4)cos80+(1/4)(cos60+cos(90+10)) =(1/4)cos80 +(1/4)(1/2-sin10) = 

(1/4)cos(90-10) +(1/4)*(1/2)-(1/4)sin10 = (1/4)sin10+1/8-(1/4sin10 =1/8 =0,125