Question

вычислите: sin(2arcctg3/4)

Answer 1

sin(2arcctg3/4) нам нужно найти Sinа

2arcctg3/4 = а

arcctg3/4 = а/2

ctg a/2 = 3/4

доведем до квадрата обе части

ctg² a/2 = (3/4)²

ctg² a/2 = 1+сosa / 1-cosa

1+сosa / 1-cosa = 9/16

25cosa = -7

cosa = -7/25

sina = √1 - 49/625 = √576/625 = 24/25

sina = 24/25

Answer 2

arcctg(3/4) = 53

sin(2*53) = sin(106) = 0.9613