Question

Determine as raízes da equação tg²x = tg x, se [0, ]

Answer 1

Resposta:

x=0

Explicação passo-a-passo:

$tg {}^{2} \times = tgx$

$\times = 0$

desculpa qualquer erro!

Answer 2

$\sf tg^2x= tg\ x \ \ ; \ \ x \in [0,\pi ] \\\\ tg^2x -tg\ x=0\\\\ tg\ x\cdot(tg\ x-1) =0 \\\\ \left\{ \begin{array}{I} \sf tg\ x = 0 \\\\ \sf x = 0 \ ou \ x = \pi \end{array}\right \\\\\\ \left\{ \begin{array}{I} \sf tgx-1 =0\to tg\ x = 1 \\\\ \displaystyle \sf x = \frac{\pi}{4} \ ou\ x = \frac{5\pi}{4} \end{array}\right \ \\\\\\ \displaystyle x = \frac{5\pi }{4}\to \begin{array}{I} \sf (N{\~A}O\ CONV{\'E}M \ J{\'A}\ QUE \ x \in [0,\pi] \ ) \end{array}$

Portanto, o conjunto solução é :

$\displaystyle \boxed{\sf x=\left\{0\ ,\ \frac{\pi}{4}\ ,\ \pi \right\} }\checkmark$