Question

se sen x = 1/3 entao sen2x vale

Answer 1

$sen(a+b) = sen(a)cos(b) + sen(b)cos(a)$

sen 2x = sen (x + x) =  senx * cos x + senx * cosx = 2* senx * cosx ( I)

sen²x + cos²x = 1 => cos x = raiz de (1 - sen²x)  = > cos x = raiz de (1 - 1/9) => cos x = raiz de (8/9) = (raiz de 8)/3

Voltando a I:
sen 2x = 2* sen x * cos x = > sen2x =  2* (1/3) * (raiz de 8)/3 = [2 (raiz de 8)]/9