Найти sin 2a, если ctg a=4/3

Question

Найти sin 2a, если ctg a=4/3

Answer 1

sin2a=2sinacosa

1+ctg^2(a) = 1/sin^2(a)
sin^2(a) = 1/(1+ctg^2(a)) = 1/(1+16/9) = 9/25
sina= +-3/5
cosa = +-√(1-sin^2(a))=+-√(1-9/25)= +-4/5

2sinacosa = 2 * 3/5 * 4/5 = 24/25 = 0.96