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
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Answers & Comments
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