Question

ctg(x+10°)=tg(x+40°) hallar x

Answer 1

Explicación paso a paso:

expresando la ecuación con una sola función trigonométrica

ctg(x+10°)=tg(x+40°)

$ctg(x+10°)=tg(x+40°) \\ ctg(x+10°) - tg(x+40°) = 0 \\ \frac{cos(x + 10)}{sen(x + 10)} - \frac{sen(x + 10)}{cos(x +10) } = 0 \\ \frac{ {cos}^{2}(x + 10) - {sen}^{2}(x + 10) }{sen(x + 10) \times cos(x + 10)} = 0 \\ 1 - {sen}^{2} (x + 10) - {sen}^{2} (x + 10) = 0 \\ 1 - 2 {sen}^{2} = 0 \\ - 2 {sen}^{2} (x + 10 = - 1 \\ {sen}^{2} (x + 10) = \frac{1}{2} \\ sen(x + 10) = + - \frac{1}{ \sqrt{2} } \\ sen(x + 10) = + - \frac{ \sqrt{2} }{2} \\ x1+ 10 = 45 \\ x1 = 45 - 10 \\ x1 = 35 \\ \\ x2 + 10 = - 45 \\ x2 = - 45 - 10 \\ x2 = - 55$