Question

A expressão: sen(2pi - x) . cos(pi + x) / tg(pi - x) . sen(pi/2 - x) , simplifique
a) cos x b) -sen c) -cos x d) sec x e) -sec x

Answer 1

$\frac{sen(2 \pi - x).cos (\pi+ x) }{tg ( \pi - x).sen( \frac{\pi} {2} - x) }$

$sen(2\pi - x)\\sen(a - b) = senacosb - senbcosa\\sen(2\pi - x) = 0.cosx - senx.1\\sen(2\pi - x) = -senx$

$cos(\pi + x)\\cos(a + b) = cosacosb - senasenb\\cos(\pi + x) = -1.cosx - 0.senx\\cos(\pi + x) = -cosx$

$tg(\pi - x)\\tg(a - b) = \frac{tga - tgb}{1 + tga.tgb}\\tg(\pi - x) = \frac{0 - tgx}{1 + 0.tgx}\\tg(\pi - x) = -tgx$

$sen( \frac{\pi}{2} - x)\\sen(a - b) = senacosb - senbcosa\\sen( \frac{\pi}{2} - x) = 1.cosx - senx.0\\sen( \frac{\pi}{2} - x) = cosx$

$\frac{(-senx).(-cosx)}{(-tgx).(cosx)}\\ (-1).\frac{senx}{tgx}\\ \frac{-senx}{tgx}\\ \frac{-sen.cosx}{senx}\\(-1).cosx = -cosx$

$Resposta: \ Alternativa \ c$