Question

tg^3a+ctg^3a = ?, tga+ctga=3

Answer 1

$tan a+cot a=3\\(tan a+cot a)^3=3^3\\ tan^3 a+3tan^2 acdotcot a+3tan acdotcot^2 a+cot ^3a=27\\tan^3 a+3tan acdotcot a (tan a+cot a)+cot^3a=27\\tan^3 a+3cdot1cdot 3+cot^3a=27\\tan^3 a+cot^3 a=18$