Question

se 0 < x < 2 e 2 sen x + cos x = 1, então tg x vale :

Answer 1

$2 sen x + cos x = 1$ → eleva-se ambos os termos ao quadrado

$(2 sen x + cos x)^{2} = 1^{2}$

$4 sen^{2} x+4senxcosx+ cos^{2} x=1$

$4 sen^{2} x+4senxcosx=1-cos^{2} x$

$4 sen^{2} x+4senxcosx=sen^{2} x$

$4senxcosx=sen^{2} x-4 sen^{2} x$

$4senxcosx=-3 sen^{2} x$

$\dfrac{senxcosx}{ sen^{2} x }= \dfrac{-3}{4}$

$\dfrac{cosx}{ senx }= \dfrac{-3}{4}$ → senx ≠ 0

$\dfrac{senx}{ cosx }= \dfrac{4}{-3}$

$tgx=- \dfrac{4}{3}$