MATH ANALYSIS
posted by anonymous on .
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

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