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solve 2sin2x = 3sinx

step by step please

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Reply 1
Avatar for Notnek
Notnek
21
Original post by piamiahh
step by step please

What have you tried so far?
Reply 2
Avatar for piamiahh
piamiahh
OP
12
step by step please
Reply 3
Avatar for S.G.
S.G.
22
Original post by piamiahh
step by step please


sin2x = 2sinxcosx

You should be able to solve it from there.
Reply 4
Avatar for piamiahh
piamiahh
OP
12
Original post by Notnek
What have you tried so far?


2(2sinxcosx)-3sinx = 0

but don't really know what can happen now
Reply 5
Avatar for Notnek
Notnek
21
Original post by piamiahh
2(2sinxcosx)-3sinx = 0

but don't really know what can happen now

So you have

4sin(x)cos(x)-3sin(x) = 0

Notice that sin(x) is a common factor so you can factorise. Try this and post your working if you get stuck.
2sin2x = 3sinx
2(2sinxcosx) - 3sinx = 0

- Started it off for you
sin2x=2sinxcosx

This should hopefully be enough.

If you forget this you have the formula sheet which says sin(A+B)=SinACosB+SinBCosA. If you input x as A and B you get sinxcos + sinxcosx which is 2sinxcosx
>inb4 divides through by sin(x)
Original post by piamiahh
2(2sinxcosx)-3sinx = 0

but don't really know what can happen now


what are the common terms between those terms, 2(2sinxcosx) = 3sinx
if you identify it, you can divide both sides from it.
Reply 10
Avatar for R0naldo
R0naldo
9
4sinxcosx-3sinx=o.
Sinx(4cosx-3)=0
Sinx=o. Cosx=3/4
Reply 11
Avatar for Notnek
Notnek
21
Original post by RDKGames
>inb4 divides through by sin(x)

Original post by YouMadBro!
what are the common terms between those terms, 2(2sinxcosx) = 3sinx
if you identify it, you can divide both sides from it.

:smile:
sinx can be taken out as a factor :-)
Reply 13
Avatar for 3121
3121
21
Original post by RDKGames
>inb4 divides through by sin(x)


You lose the sinx solutions if you do that, you’ll only get the ones for cosx unless you meant factor out
Reply 14
Avatar for piamiahh
piamiahh
OP
12
Original post by Notnek
So you have

4sin(x)cos(x)-3sin(x) = 0

Notice that sin(x) is a common factor so you can factorise. Try this and post your working if you get stuck.


got it! thank you!!
Original post by Notnek
:smile:


Bound to happen on EVERY.SINGLE.THREAD :lol:
Original post by Zxyn
You lose the sinx solutions if you do that, you’ll only get the ones for cosx unless you meant factor out


It was a joke.
I got sinx = 0 and 4cosx=3
cosx = 3 divided by 4

is this correct...

i'm in gcse
4C9D188D-705B-4A4F-805E-FE5452E24B0F.jpg.jpeg hope this helps

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