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STEP I 2003 - Q3 part (i)

Please can someone go through the answer to this question. Or present the answer, but saying exactly what they are doing at each step and how they got each term. Because I looked at the solution on here and I didn't really understand it.

The link to the paper is:
https://docs.google.com/file/d/0B-C3uSoohVKqM1hUbVFITjNTcWlweU1QSVJMS3FwZw/edit?pli=1
Do you understand that to do this question you need to show that both sin (x/2) = 0 implies 2 sin (x/2) = sin x and 2 sin (x/2) = sin x implies sin (x/2) = 0?
Original post by electriic_ink
Do you understand that to do this question you need to show that both sin (x/2) = 0 implies 2 sin (x/2) = sin x and 2 sin (x/2) = sin x implies sin (x/2) = 0?


Is that because it is an 'if and only if'?
I think my main issue is that I don't understand (on the first line) where he got 2sin(x/2)=2sin(x/2)cos(x/2).
And then I can follow most of it until the second to last line.
Original post by brittanna
Is that because it is an 'if and only if'?


Yeah.

Original post by brittanna
I think my main issue is that I don't understand (on the first line) where he got 2sin(x/2)=2sin(x/2)cos(x/2).
And then I can follow most of it until the second to last line.


sin x = 2sin(x/2)cos(x/2) (double angle formula)
I understand the double angle formula bit, but why does sin(x)=2sin(x/2)?
Original post by brittanna
I understand the double angle formula bit, but why does sin(x)=2sin(x/2)?


If sin (x/2) = 0, sin x = 2 sin (x/2) cos (x/2) = 0 and 2 sin (x/2) = 0. Since both are zero, sin(x)=2sin(x/2).
Original post by electriic_ink
If sin (x/2) = 0, sin x = 2 sin (x/2) cos (x/2) = 0 and 2 sin (x/2) = 0. Since both are zero, sin(x)=2sin(x/2).


Thank you. I think I understand it now. I may have a few more questions in 10 minutes or so though :biggrin:.

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