Question

qual conjunto solucao de sen x - cos x = 0 em 0,2 pi?

Answer 1

$\sin(x) - \cos(x) = 0 \\ {( \sin(x) - \cos(x))}^{2} = {0}^{2} \\ { \sin }^{2} x - 2 \sin(x). \cos(x) + { \cos }^{2}x \\ = 0$

${ \sin}^{2}x + { \cos}^{2}x - 2 \sin(x) \cos(x) \\ = 0$

$1 - \sin(2x) = 0 \\ \sin(2x) = 1 \\ \sin(2x) = \sin( \frac{\pi}{2} ) \\ 2x = \frac{\pi}{2}$

$x = \frac{1}{2} . \frac{\pi}{2} \\ x = \frac{\pi}{4}$