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    Suppose z = cosx + isinx, express cos4x in terms of z

    No idea what i am doing.

    i thought this question was asking me to write it in terms of cosx

    So i have cos^4(x) - 6cos^2(x)sin^2(x) + sin^4(x)

    Absolutely lost, pls help.
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    You can put the sin^2(x) in terms of cos^2(x) using C2 trig identities. The sin^4x is similar except you need to square the identity. Sorry for not giving the identity, I think I have to only give hints XD
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    (Original post by BinaryJava)
    You can put the sin^2(x) in terms of cos^2(x) using C2 trig identities. The sin^4x is similar except you need to square the identity. Sorry for not giving the identity, I think I have to only give hints XD
    Hiya, i have simplified it to 8cos^4(x) - 8cos^2(x) + 1

    This is my maximum
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    (Original post by Bobjim12)
    Hiya, i have simplified it to 8cos^4(x) - 8cos^2(x) + 1

    This is my maximum
    Yeah that is what I got. Do you know if we need to know the proof by induction for de moivres theorem?
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    (Original post by BinaryJava)
    Yeah that is what I got. Do you know if we need to know the proof by induction for de moivres theorem?
    I don't think so,

    the answer is 1/2(z^4 + 1/z^4)............................ ..

    There isn't an example in my textbook so i haven't a clue what i am doing..
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    Do you know what, i am stupid. Never mind, i have got it now, thankyou though for trying :^)
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    I guess then you let cos4x = z which is the same as z^4 = cosx. Not sure about where the 8 goes though.
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    (Original post by BinaryJava)
    Yeah that is what I got. Do you know if we need to know the proof by induction for de moivres theorem?
    For edexcel you do
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    (Original post by BinaryJava)
    I guess then you let cos4x = z which is the same as z^4 = cosx. Not sure about where the 8 goes though.
    yes i was being silly, thankyou
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    (Original post by Gome44)
    For edexcel you do
    Damn thought I got away from that induction rubbish, seems simple enough.
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    (Original post by Bobjim12)
    Suppose z = cosx + isinx, express cos4x in terms of z

    No idea what i am doing.

    i thought this question was asking me to write it in terms of cosx

    So i have cos^4(x) - 6cos^2(x)sin^2(x) + sin^4(x)

    Absolutely lost, pls help.
    Note that z^{-1} = (\cos x +i \sin x )^{-1} = \cos x - i \sin x. How can you then express \cos x in terms of z (and z^{-1})?

    Now use De Moivre's Theorem to do something similar with \cos 4x
 
 
 
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