Question

$tga+ctga+tg3a+ctg3a= frac{8 cos^{2}2a }{sin6a}$
доказать тождество

Answer 1

tga+tgb=sin(a+b)/(cosa*cosb)
ctga+ctgb=sin(a+b)/(sina*sinb)
sin(a+3a)/cosacos3a+sin(a+3a)/sinasin3a=
=sin4a(sinasin3a+cosacos3a)/sinasin3acosacos3a=
=4sin4acos(3a-a)/sin2asin6a=
=4*2sin2acos2acos2a/sin2asin6a=8cos²a/sin6a