Question

если tg (альфа+n/4)=-1/3, то значение ctg2альфа равно

Answer 1

tg(a + π/4) = (tg a + tgπ/4)/(1 - tg a tgπ/4) = (tg a +1)/(1 - tg a)= -1/3
3(tga +1) = -1  + tga
3tga + 3 = -1 + tga
2tg a = -4
tg a = -2
tg 2a = 2tg a/(1 - tg²a) = -4/(1 - 4) = 4/3
Сtg 2a = 3/4