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

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

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

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

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

because sinx=2sin1/2xcos1/2x

hope it is clear

no im very confused...=(

sin2x=2sinxcosx

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

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

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)

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