Question

Se $senx + cosx = \frac{1}{\sqrt{3} }$, calcule $sen2x$

Answer 1

Use que:

sen²x + cos²x = 1

sen2x = 2senxcosx

senx + cosx = 1/√3

(senx + cosx)² = (1/√3)²

sen²x + cos²x + 2senxcosx = 1/3

1 + 2senxcosx = 1/3

2senxcosx = 1/3

2senxcosx = 1 - 1/3

2senxcosx = 2/3 = sen2x

Resposta: 2/3