Question

how did this step come about? from
4sin1/2xcos1/2x
=2sinx

Answer 1

This is a trigonometric identity. Best know as sin2x=2sinxcosx

Answer 2

ok.. since sin2x=2sinxcosx,
then isn't sin1/2x=2sin1/2xcos1/2x?

Answer 3

no
sin1/2x=2sin1/4xcos1/4x

Answer 4

then why 4sin1/2xcos1/2x
=2sinx

Answer 5

because sinx=2sin1/2xcos1/2x

Answer 6

hope it is clear

Answer 7

no im very confused...=(

Answer 8

sin2x=2sinxcosx

Answer 9

why sin x becomes 2sin1/2xcos1/2x?
did you replace x

Answer 10

you have sin2x=2sinxcosx
so what happens is that you multiply by two
than for the sincos part you divide by two to get from sin2x=2sinxcosx

so
sinx=2*
the sincos part you have to devide by two
that is sin1/2xcos1/2x

so sinx=2sin1/2xcos1/2x

Answer 11

First, 2sin(x) cos(x)= sin(2x) comes from sin(A+B)= sin(A)cos(B)+sin(B)cos(A)
for sin(A+B) proof see http://www.youtube.com/watch?v=zw0waJCEc-w

now for your particular problem
\[4sin(x/2)cos(x/2)=2⋅(2sin(x/2)cos(x/2))\]

2⋅(2sin(x/2)cos(x/2))=2⋅(sin(2⋅x/2)=2sin(x)