Question

2sin(pi/4+x)sin(pi/4-x)=?

Answer 1

See
http://www.math.missouri.edu/escgi/mucgi-bin/trigidentities.cgi
Product To Sum Formulas

Answer 2

\[
2 \sin(a) \sin(b)= \cos(a-b) - \cos(a+b)
\]

Answer 3

\[
2\sin(\pi/4 + x) \sin(\pi/4 -x)= \cos(2x) -\cos(\pi/2)=\cos(2x)
\]