Question

докажите тождество (cos^2 A ) / (tg A/2 - ctg A/2) = (-1/4 sin2A)

Answer 1

cos²a/(tga/2-ctga/2)=-1/4*sin2a
1)tga/2-ctga/2=(sina/2*sina/2-cosa/2*cossa/2)/
(sina/2*cosa/2)=(sina/2)²-(cosa/2)²/1/2(2sina/2*cosa/2=-cosa/1/2*sina=-2cosa/sina
2)cos²a:(-2cosa/sina)=-1/2sina*cosa=
-1/4(2sina*cosa)=-1/4*sin2a