MATH ANALYSIS

How do you simplify these questions?:
1. cos^2(x/2)-sin^2(x/2)

2. 2cos^2(3A)-1

3. sin 2x/1+cos2x

I think number 3 is tan 2x?

The other two I don't know.
Thanks for the help

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  1. It looks like you are working with the expansions of
    sin 2A and cos 2A, and are expected to know those formulas

    1. is a direct result of the expansion of
    cos 2A = cos^2 A - sin^2 A
    so cos^2(x/2)-sin^2(x/2) = cosx

    2. again, direct application
    2cos^2(3A)-1 = cos 6A

    3. sin 2x/1+cos2x
    = 2sinxcosx/(1 + cos^2 x - sin^2 x)
    = 2sinxcosx(cos^2 x + cos^2 x)
    = 2sinxcosx/(2cos^2 x)
    = sinx/cosx
    = tanx

    You had tan 2x

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