Triangle innequality proof question

[transgalactic]

for "a" and "b" are real numbers prove that:

http://img352.imageshack.us/my.php?image=34860604zw7.gif

i need to use the triangle innequality
|a|-|b|=< |a+b| <= |a| + |b|

how to apply it to my question?
it a long way from
triangle innequality formula to the expression that i was given in the question

??

 

[Pere Callahan]

The triangle inequality reads

|x+y|<=|x|+|y|
or
|x|>=|x+y|-|y|

for any two vectors x,y

Take in particular

x=a-b, y=b

and

x=b-a, y=a

What do you get?
Then use, |a-b|=|b-a| and the fact that if |a-b| is greater than c and greater then -c, it must be greater than |c|. (What is c?)