Principle Of Mathematical Induction

Question
CBSEENMA11014300

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

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