Posted by **anonymous** on Tuesday, May 25, 2010 at 1:02am.

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

- MATH ANALYSIS -
**Reiny**, Tuesday, May 25, 2010 at 7:11am
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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