Question

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Find all solutions in the interval [0, 2π).

2 sin2x = sin x

Answer 1

@PFEH.1999

Answer 2

2 sin^2x = sin x****

Answer 3

@bina_love do you know hot to solve this?

Answer 4

@hartnn

Answer 5

subtract sin x from both sides
and factor it out from the left

Answer 6

These are my answer choices
A. x = pi/3 , 2pi/3
B. x = pi/2 , 3pi/2 , pi/3 , 2pi/3
C. x = 0 , pi , pi/6 , 5pi/6
D. x = pi/6 , 5pi/6

Answer 7

I dont see how i can get any of those answers from doing what you told me to do? @hartnn

Answer 8

i'll tell you how, firstly
could you do what i said ?

Answer 9

I would be left with 2 sin x correct?

Answer 10

what did u get after subtracting sin x from bot hsides ?

Answer 11

2 sin x?

Answer 12

noooo...

2sin^2 x = sin x
so, 2 sin^2 x - sin x = 0

now factor out sin x from here

Answer 13

i should end up with x ( 2x -1 ) = 0 correct?

Answer 14

yeah, actually sin x (2 sin x-1) = 0
thats the factored form

Answer 15

so either sin x = 0
or 2 sin x -1 = 0

got this ?

Answer 16

Yeah okay now what

Answer 17

when will sin x be = 0 ?

Answer 18

Im not sure, can you just show me how to do it step by step and then ill ask you uestions afterwards? This is going to take forever, its just a practice problem regardless.

Answer 19

Questions*

Answer 20

sin x will be 0 when x=0 !!
or x= pi, 2pi ...

Answer 21

But thats not one of my answer choices?

Answer 22

in 0 to 2pi we will have 0 and pi

now, for 2sin x -1=0
sin x =1/2 , right ??

for which angles will sin x be = 1/2 ??

Answer 23

x?

Answer 24

i asked for which angles ?

ok, sin x is 1/2 for x = pi/6 , 5pi/6
so our 4 angles will be

x = 0 , pi , pi/6 , 5pi/6

Answer 25

Thank you so much