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Principle Of Mathematical Induction

Question

Prove the following:

$cos left parenthesis 2 straight pi plus straight x right parenthesis space equals space cosx$

Solution

As cosx is a periodic function of period $2 straight pi$ . Hence, an integral multiple of $2 straight pi$ can be added or subtracted from the angle.
$cos left parenthesis 2 straight pi plus straight x right parenthesis equals cos left parenthesis 2 straight pi plus straight x minus 2 straight pi right parenthesis equals cosx$
Hence, $cos left parenthesis 2 straight pi plus straight x right parenthesis space equals space cosx$