Question

2
Ecuaciones Trigonometricas
atividades
a) 2cos²x=2 - senx
b) 3 tan x= 2 cos x
C) 2 sen x = cosec X
D) 2 cos x + 1= 0​

Answer 1

Respuesta:

Explicación paso a paso:

a) 2cos²x=2 - senx

$2(1-sen^2x)=2-senx\\2-2sen^2x=2-senx\\senx-2sen^2x=0\\senx(1-2senx)=0$

$senx=0$ ∨ $1-2senx=0$

$senx=0$ ∨ $senx=\frac{1}{2}$

3 tan x= 2 cos x

$\frac{3senx}{conx} =2cosx\\3senx=2cos^2x\\3senx=2(1-sen^2x)\\3senx=2-2sen^2x\\2sen^2x+3senx-2=0\\(senx+2)(2senx-1)=0$

senx=-2 ∨ senx=1/2

C) 2 sen x = cosecx

$2senx=\frac{1}{senx}$

$2sen^2x=1\\2sen^2x-1=0\\(\sqrt{2} senx+1)(\sqrt{2} senx-1)=0$

senx=$\frac{-1}{\sqrt{2} }$ v senx=$\frac{1}{\sqrt{2} }$

D) 2 cos x + 1= 0​

cosx=-1/2