Question

como resolver senB.cosB=1/2

Answer 1

 Olá!

$\\ \sin \beta \cdot \cos \beta = \frac{1}{2} \\\\ 2 \cdot \sin \beta \cdot \cos \beta = 1 \\\\ \sin (2\beta) = 1$

 Afim de visualizar melhor o que está a acontecer, tome $2\beta = \alpha$.

 Daí,

$\\ \sin (2\beta) = 1 \\ \sin \alpha = 1 \\ \alpha = \frac{\pi}{2}$

 Portanto, temos que:

$\\ 2\beta = \alpha \\\\ 2\beta = \frac{\pi}{2} \\\\ \boxed{\beta = \frac{\pi}{4}}$

 Na verdade, $\boxed{\boxed{\beta = \frac{\pi}{4} + 2\pi \cdot k}}$, onde $k \in \mathbb{Z}_+$.