Question

Доказать тождество: $tg\alpha + ctg\alpha + tg3\alpha +ctg3\alpha = \frac{8cos20\alpha }{sin6\alpha }$

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