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

MATH ANALYSIS 
Reiny,
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