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1 - cos2x

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    is

    1 - cos2x equal to (sinx)^2

    ??????thanks:confused:
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    Nearly. It's equal to 2(sinx)^2. Proof is from the double angle formula.
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    No

    Rule is

    cos^2 x + sin^2 x =1
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    (Original post by tommm)
    Nearly. It's equal to 2(sinx)^2. Proof is from the double angle formula.
    thanks.

    is that just one of the ones we have to remember?
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    (Original post by rye225)
    No

    Rule is

    cos^2 x + sin^2 x =1
    You're thinking of the wrong rule; the rule you want is the double angle formula for cosine.

    (Original post by sonic23)
    thanks.

    is that just one of the ones we have to remember?
    You're given \cos (A+B) = \cos A \cos B - \sin A \sin B, so you can derive \cos 2x = \cos^2 x - \sin^2 x and play with it until you get it in the right form... but it's worth remembering these three, if nothing else:
    \newline \cos 2x = \cos^2 x - \sin^2 x\newline

= 2\cos^2 x - 1\newline

= 1 - 2\sin^2 x

    Then you can rearrange it.
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    (Original post by sonic23)
    thanks.

    is that just one of the ones we have to remember?
    Pretty much, yes. As an experienced A-leveller, I can immediately recall \cos 2x = 2 \cos^2 x - 1 = \cos^2 x - \sin^2 x = 1 - 2 \sin^2 x, but that's because I've used it so many times. Practice makes perfect.
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    (Original post by nuodai)
    You're thinking of the wrong rule; the rule you want is the double angle formula for cosine.


    You're given \cos (A+B) = \cos A \cos B - \sin A \sin B, so you can derive \cos 2x = \cos^2 x - \sin^2 x and play with it until you get it in the right form... but it's worth remembering these three, if nothing else:
    \newline \cos 2x = \cos^2 x - \sin^2 x\newline

= 2\cos^2 x - 1\newline

= 1 - 2\sin^2 x

    Then you can rearrange it.

    thanks
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    Not a problem.

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Updated: March 3, 2009
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