Question

Нужно пошагово упростить уравнение

Answer 1

(tga-ctga)/(tga+ctga)=(sina/cosa-cosa/sina):(sina/cosa+cosa/sina)=
=(sin²a-cos²a)/(sinacosa) :(sin²a+cos²a)/(sinacosa)=
-cos2a/(sinacosa)*(sinacosa)/1=-cos2a

Answer 2

tg = sin / cos
ctg = cos / sin
cos² x - sin² x = cos (2x)
sin² x + cos² x = 1
tg(a) - ctg(a) = sin(a)/cos(a) - cos(a)/sin(a) = (sin²(a) - cos²(a))/sin(a)cos(a)= - cos(2x)/sin(a)cos(a)
tg(a) + ctg(a) = sin(a)/cos(a) + cos(a)/sin(a) = (sin²(a) + cos²(a))/sin(a)cos(a)= 1 /sin(a)cos(a)
- cos(2x)/sin(a)cos(a) / 1 /sin(a)cos(a) = - cos(2x)/sin(a)cos(a) * sin(a)cos(a)/1 = -cos(2a)