Question

(Carlos Chagas-SP) Se 0<x<π, e
$\left[\begin{array}{ccc}1&cosx&0\\senx&0&1\\senx&0&-1\end{array}\right]$ = 1/2 então o valor de x é:

a)π/6 ou 5π/6           b)π/3 ou 4π/3

c)π/3 ou 2π/3           d)π/6 ou 2π/3      e)π/12 ou 5π/12 

Answer 1

$Resolu\c{c}\~ao\to \left|\begin{array}{ccc}1&cosx&0\\senx&0&1\\senx&0&-1 \end{array}\right| \to 2*cosx*senx = \frac{1}{2} \\\\\\ Resolu\c{c}\~ao\to \left\{\begin{array}{ccc}2*cosx*senx = \frac{1}{2} \\\\sen(2x) = \frac{1}{2} \\\\2x = 30^o\\\\\boxed{x = 15^o} \\\\Letra\ A\\( \frac{\pi}{6}\ ou\ \frac{5\pi}{6})\to (30^o\ ou\ 150^o) } \end{array}\right$

Espero ter ajudado. :))