( tg a+ctg )^{2} - ( tg a - ctg )^{2}

Question

( tg a+ctg )^{2} - ( tg a - ctg )^{2}

Answer 1

(tgα+ctgα)^2-(tgα-ctgα)^2 = tg²α+2tgαctgα+ctg²α-(tg²α-2tgαctgα+ctg²α)=

= tg²α+2tgαctgα+ctg²α - tg²α+2tgαctgα-ctg²α = 4tgαctgα = 4

 

ОТВЕТ: 4

Answer 2

( tg a+ctg )^{2} - ( tg a - ctg )^{2}=(tg a+1/tg)^2-(tg a - 1/tg a)^2=((tga^2+1)^2-(tga^2-1)^2)/tga^2=4