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    Hi everyone,

    I've got a two part question that I'm struggling with. The first part, which I'm assuming is relevant to the second part is:

    Show  3 \sin \theta = 2 \cos^2 = 0 . I did this fine using the id  tanx = \frac{sinx}{cosx}

    I'm stuck on the second part though, and I'd be really appreciative if anyone could help. It is:

    Hence, use an appropriate identity to show that  2 \sin^2 \theta + 3 \sin \theta - 2 = 0 . To be honest, I'm not sure where to start!
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    (Original post by marcsaccount)
    Hi everyone,

    I've got a two part question that I'm struggling with. The first part, which I'm assuming is relevant to the second part is:

    Show  3 \sin \theta = 2 \cos^2 = 0 . I did this fine using the id  tanx = \frac{sinx}{cosx}

    I'm stuck on the second part though, and I'd be really appreciative if anyone could help. It is:

    Hence, use an appropriate identity to show that  2 \sin^2 \theta + 3 \sin \theta - 2 = 0 . To be honest, I'm not sure where to start!
    \sin^2 x + \cos^2 x =1
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    (Original post by Mr M)
    \sin^2 x + \cos^2 x =1

    Hi MrM, I thought about using that ID initially but that just gave me  2(1- \cos^2 \theta ) + 3 \sin \theta - 2 and I wasn't sure how to progress from there.
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    (Original post by marcsaccount)
    Hi MrM, I thought about using that ID initially but that just gave me  2(1- \cos^2 \theta ) + 3 \sin \theta - 2 and I wasn't sure how to progress from there.
    You've made a mistake there. Look again. You need to substitute into the first identity.

    Obviously your version will simplify to the first if you expand the bracket but it is a peculiar way to do it.
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    (Original post by marcsaccount)
    Hi MrM, I thought about using that ID initially but that just gave me  2(1- \cos^2 \theta ) + 3 \sin \theta - 2 and I wasn't sure how to progress from there.
    3sinx= 2cos^2x
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    (Original post by Mr M)
    You've made a mistake there. Look again. You need to substitute into the first identity.

    Obviously your version will simplify to the first if you expand the bracket but it is a peculiar way to do it.
    The first identity being tanx=(sanx)/(cosx)?

    I'm really confused!
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    (Original post by marcsaccount)
    The first identity being tanx=(sanx)/(cosx)?

    I'm really confused!
    3 \sin x - 2 \cos^2 x = 0

    (your version is a bit mangled)

    3 \sin x - 2 (1 - \sin^2 x) = 0

    Expand the bracket.
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    (Original post by marcsaccount)
    Hi MrM, I thought about using that ID initially but that just gave me  2(1- \cos^2 \theta ) + 3 \sin \theta - 2 and I wasn't sure how to progress from there.
    Multiply out the brackets and you get what you got in part a).

    You just proved this is equal to 0, so it's done.
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    (Original post by Mr M)
    3 \sin x - 2 \cos^2 x = 0

    (your version is a bit mangled)

    3 \sin x - 2 (1 - \sin^2 x) = 0

    Expand the bracket.
    3 \sin x - 2 (1 - \sin^2 x) = 0

 2 \sin^2 x + 3 \sin x - 2

    Should I factorise it? I'm just not sure what the aim is?!
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    Actually factorising is the next part so I shouldn't do that now. I still don't know what I'm supposed to do with it to prove it equals zero.

    p.s. thanks for helping me!
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    (Original post by tomtjl)
    Multiply out the brackets and you get what you got in part a).

    You just proved this is equal to 0, so it's done.
    3 \sin x - 2 (1 - \sin^2 x) = 0

2 \sin^2 x + 3 \sin x - 2

    So this is the answer? How does it prove it is equal to zero though? It looks different to what I got in part A...
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    Sorry everyone! I've seen it now. For some reason I just couldn't spot it at first. Thanks for all your help.

    Marc
 
 
 
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