Matilde

Il valore di # (cos (pi / 12) -sin (pi / 12)) (tan (pi / 12) + cos (pi / 12)) # ?? # (cos (pi/12)-sin (pi/12))(tan (pi/12)+cos( pi/12) )# #= (cos (pi/12)/cos (pi/12)-sin (pi/12)/cos (pi/12))cos (pi/12)(tan (pi/12)+cos( pi/12) )# #=(1-tan(pi/12))(sin(pi/12)+cos^2(pi/12))# #=(1-tan(pi/12))(sin(pi/12)+1/2(1+cos(pi/6))# #=(1-tan(pi/12))(sin(pi/12)+1/2(1+cos(pi/6))# Adesso #tan(pi/12)=tan(pi/3-pi/4)# #=(tan(pi/3)-tan(pi/4))/(1+tan(pi/3)tan(pi/4))=(sqrt3-1)/(sqrt3+1)# Di nuovo #sin(pi/12)# #=sin(pi/3-pi/4)# #=sin(pi/3)cos(pi/4)-cos(pi/3)sin(pi/4)# #=(sqrt3-1)/(2sqrt2)# So #(1-tan(pi/12))(sin(pi/12)+1/2(1+cos(pi/6))# #=(1-(sqrt3-1)/(sqrt3+1))((sqrt3-1)/(2sqrt2)+1/2(1+sqrt3/2))# … Leggi tutto