Question

сtg40*tg140=

cos79*cos34+sin79*sin34=

если можно с объяснением

Answer 1

ctg40*tg140=cos(79-34)

ctg40*tg140=cos45

cos40/sin40*sin140/cos140=sqrt2/2

cos40/sin40*cos40/sin40=sqrt2/2

ctg^2(40)=sqrt2/2

 

Answer 2

cosalfa*cosbeta+sinalfa*sinbeta=cos(alfa-beta)cos79*cos34+sin79*sin34=cos(79-34)=cos45=sqrt(2)/2.  cosalfa*sinbeta=1/2*( sin(alfa-beta) + sin(alfa+beta)) ctg40*tg140=cos40/sin40 * sin140/cos140= (cos40*sin140)/(sin40*cos140)==[1/2 * (sin(40-140)+sin(40+140))]/[1/2 * (sin(140-40)+sin(140+40)] =(sin(-100)+sin180)/(sin100+sin180)= - sin100/sin100= -1