Question

Resolver a equação senx + cosx = 0, em R:

Answer 1

Resposta:

senx + cosx = 0

(senx + cosx)² = 0

sen²x + 2senxcosx + cos²x = 0

sen2x = -1

sen2x = sen(270)

2x = 270

x = 135°

Answer 2

$\displaystyle \sf sen(x) +cos(x) = 0 \\\\ sen(x) = -cos(x)\ \ \div{cos(x)} \\\\ \frac{sen(x)}{cos(x)}= \frac{-cos(x)}{cos(x)} \\\\ \\\ tg(x) = - 1 \\\\ tg(x) = tg\left(\frac{3\pi }{4} +k\cdot \pi \right) \\\\\\ portanto : \\\\\ \huge\boxed{\sf \ x = \frac{3\pi }{4}+k\cdot \pi \ \ , \ k\in\mathbb{Z} \ }\checkmark$