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show that cos(pi x) = pi cosx is not an identity by finding a single value of x for which it fails to hold.

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How about the most obvious case, x - 0

LS = cos (π(0)) = cos 0 = 1
RS = 0(cos0) = 0(1) = 0 ≠ LS

Now, a more interesting question would have been ,
For what values of x is the statement true?

http://www.wolframalpha.com/input/?i=cos%28πx%29+%3D+π*cos%28x%29
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