Question

tan=2sin

Answer 1

your attempt?

Answer 2

sin/cos=2sin
cos*sin/cos=2sin*cos
0=2sin*cos-sin

Answer 3

i don't know where to go from there

Answer 4

go ahead, very good, factor sin out

Answer 5

so would it be
0=sin*cos

Answer 6

2sin cos - sin =0
sin(2cos -1) =0
sin =0 or 2cos-1 =0
can step up?

Answer 7

this is where i am confused how do you get the 2 cos-1?

Answer 8

you have \(2sin (x) cos (x) - sin(x) =0\) right?

Answer 9

yes

Answer 10

I factor sin(x) out
it turns to \(sin(x) (2cos(x) -1) =0\)

Answer 11

got it?

Answer 12

\[\color{red}{sin(x)}2cos(x)-\color{red}{sin(x)}=0\]

Answer 13

ok, so you pull out a sin and the other sin becomes cos-1 and that is where the 2cos comes from

Answer 14

factor sin out
\[\color{red}{sin(x)}(2cos(x)-1)=0\]

Answer 15

hey, at the beginning, your right hand side is 2 sin, I do nothing on it

Answer 16

ok, I re-write it

Answer 17

tan x = 2 sin x, right?
\(\dfrac{sin(x)}{cos(x)}= 2sin (x)\) ok?

Answer 18

yes

Answer 19

with the condition of \(x\neq \pi/2\) for cos (x)\(\neq 0\)

Answer 20

you can move cos x to the right side and get
sinx = 2 sin x cos x, right?

Answer 21

yes or no?

Answer 22

ok

Answer 23

yes

Answer 24

now, take all to the right hand side to get 2sin cos -sin =0

Answer 25

yes

Answer 26

then, get the step above

Answer 27

ok i understand now thanks !!

Answer 28

ok