tg2x=3/4 п<x<5п/4 найти: cos x sin x tg x ctg x

Question

tg2x=3/4 п

найти:

cos x

sin x

tg x

ctg x

Answer 1

Cost = 3/4 cos(t/2) = ((1 + cost)/2)^(1/2) = ((1 + 3/4)/2)^(1/2) = (7/8)^(1/2) = (7^(1/2))/(2*(2^(1/2))) sin(t/2) = (1 - cos^2(t/2))^(1/2) = (1 - 7/8)^(1/2) = 1/(8^(1/2)) = 1/(2*(2^(1/2))) tg(t/2) = sin(t/2)/cos(t/2) = (1/(2*(2^(1/2))))/((7^(1/2))/(2*(2^(1/2)))) = 1/(7^(1/2)) ctg(t/2) = 1/tg(t/2) = 7^(1/2)