Question

Solve: sin x + sin 2x = 0

Answer 1

break down sin2x into 2sinxcosx
sinx+2sinxcosx=0
sinx(1+2cosx)=0
sinx=0 or 1+2cosx=0
sinx=0 or cosx=-1/2

Answer 2

where did you get the (1+2cosx) from ?

Answer 3

sinx + 2 sinx cos x = 0
sin x ( 1 + 2 cos x) = 0
sinx = 0 , cos x = -1/2
for x between 0 and 360

x = 0, 180, 360, 120, 240 degrees

Answer 4

i factored out a sinx from each term on the left

Answer 5

can you please explain it more?

Answer 6

sin(2x)=2sin(x)*cos(x)

Answer 7

Rewrite the equation with this in mind

Answer 8

sin(x)+2sin(x)*cos(x)=0

Answer 9

ok

Answer 10

Now you can factor out a sin(x) from each term

Answer 11

sin(x)[1+2cos(x)]=0

Answer 12

if you were to distribute the sin(x), you'd get back to
sin(x)+2sin(x)cos(x)=0

Answer 13

that's just explaining how it was factored, don't distribute it

Answer 14

understand that?

Answer 15

hmm it is kinda confusing, I'm still trying to understand, sorry I'm kinda slow :(

Answer 16

suppose we let sinx=a and cosx=b

Answer 17

a+2ab=0

Answer 18

i get the part sin x + 2sinxcosx = 0 it's in the book

Answer 19

a(1+2b)=0

Answer 20

but i dont get the part (1+2cos x) from ?

Answer 21

replace a and b with the values we substituted them for
sinx(1+2cosx)=0