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    Please help me... I'm stuck
    Thank you
    cos^4 theta + 2sin^2 theta + sin^4 theta
    So far I've done:
    Cos^2 theta (cos^2 theta +1) + sin^2 theta ( 2+ sin^2)
    (Cos ^2 theta)( sin^2 theta) = (2+sin^2)(cos^2 theta +1)
    Cos^2 sin^2 theta= 2cos^2 theta + 2 + sin^2 cos ^2 theta + sin^2
    Cos^2sin^2 theta= 2cos^4 2theta + sin^4 +2
    Cos^2 2 theta + sin^2 theta +2
    Cos^2 2 theta + sin^2 theta + 2 = 1
    Answer is 1
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    Can you explain your first line? There's issues beyond that but your initial assertion (?) of \cos^4 \theta + 2\sin^2\theta +\sin^4\theta \equiv \cos^2\theta(\cos^2\theta+1) + \sin^2\theta(2+\sin^2\theta) is incorrect. Perhaps you added a +1 in the first brackets by mistake? I'm not sure where you're going with the rest.

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    also pings to move this to the correct section Sonechka Lemur14

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    (Original post by _gcx)
    Can you explain your first line? There's issues beyond that but your initial assertion (?) of \cos^4 \theta + 2\sin^2\theta +\sin^4\theta \equiv \cos^2\theta(\cos^2\theta+1) + \sin^2\theta(2+\sin^2\theta) is incorrect. Perhaps you added a +1 in the first brackets by mistake? I'm not sure where you're going with the rest.

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    also pings to move this to the correct section Sonechka Lemur14


    Oops I think I wrote it wrong
    The question is:
    Simplify the following expressions:
    Cos^4 theta + 2sin^2 theta cos^2 theta + sin^4 theta
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    (Original post by Musicanor)
    Oops I think I wrote it wrong
    The question is:
    Simplify the following expressions:
    Cos^4 theta + 2sin^2 theta cos^2 theta + sin^4 theta
    In that case your final answer is correct, but you have some mistakes in your working. (I'm not sure how you reached your conclusion from your last few lines. If you graph y=\cos^2 2x + \sin^2x + 2 you'll see that it's neither constant nor equal to 1) It's easier to factorise. We have (\cos^2\theta)^2 + 2\sin^2\theta\cos^2\theta + (\sin^2\theta)^2. Does this look familiar?
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    (Original post by _gcx)
    In that case your final answer is correct, but you have some mistakes in your working. (I'm not sure how you reached your conclusion from your last few lines. If you graph y=\cos^2 2x + \sin^2x + 2 you'll see that it's neither constant nor equal to 1) It's easier to factorise. We have (\cos^2\theta)^2 + 2\sin^2\theta\cos^2\theta + (\sin^2\theta)^2. Does this look familiar?
    mmmm...
    cos 2 θ − sin 2 θ = 1 − 2 sin 2 θ ????
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    (Original post by Musicanor)
    mmmm...
    cos 2 θ − sin 2 θ = 1 − 2 sin 2 θ ????
    No, that's not true, (that is, it isn't an identity) unless you mean \cos^2 etc.

    Try expanding (x^2+y^2)^2. What do you see?
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    (Original post by _gcx)
    No, that's not true, (that is, it isn't an identity) unless you mean \cos^2 etc.

    Try expanding (x^2+y^2)^2. What do you see?
    X^4 +y^4 + x^4y^4
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    (Original post by Musicanor)
    X^4 +y^4 + x^4y^4
    Or is it 2x^4 +2x^4 2y^4 +2y^4
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    (Original post by Musicanor)
    X^4 +y^4 + x^4y^4
    You should be comfortable with this,

    (x^2 + y^2)^2 \equiv (x^2)^2 + 2x^2y^2 + (y^2)^2 \equiv x^4 + 2x^2y^2 + y^4

    You have \sin^4\theta + 2\sin^2\theta\cos^2\theta + \cos^4\theta
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    (Original post by _gcx)
    You should be comfortable with this,

    (x^2 + y^2)^2 \equiv (x^2)^2 + 2x^2y^2 + (y^2)^2 \equiv x^4 + 2x^2y^2 + y^4

    You have \sin^4\theta + 2\sin^2\theta\cos^2\theta + \cos^4\theta
    Thanks.
 
 
 
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