Have you tried adding a xml:space="preserve" attribute and use just plain normal line breaks?
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2349answers:
3Why not use regular linebreaks? Those work just fine.
If you want <br /> to appear, you need to encode those entities:
<br />
From the DTD:
<!ELEMENT TEXTAREA - - (#PCDATA) -- multi-line text field -->
In the XHTML code of your page, a <textarea> can only contain text (#PCDATA), and you cannot nest any XHTML elements within the <textarea>.
Your questions seems to show two different things. The image shows "<br />" written into a <textarea>, while the message from the W3C Validator is referring to a <br /> element written into the XHTML of your page within the <textarea> element.
In the first case, having "Test<br />line break" appear to the user in the text area is done by using the appropriate entities, just as altCognito wrote:
<textarea>Test<br />line break</textarea>
Anything that's being entered by the user that is then redisplayed within a <textarea> on a new page should be encoded (i.e., use entities for &, ", ', <, and >).
If want to display a user's entry:
Test
<br />line break
...as...
Test
line break
...within another text area, then you will need to parse what has been entered into the original <textarea> and replace the user-entered <br />s with normal line breaks. See Lucero's answer.