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Answer :

Answer: [tex]-\csc x[/tex]

Step-by-step explanation:

I will be writing 'csc' instead of 'cosec'.

Since [tex]\csc x[/tex] has a period of [tex]2\pi[/tex],

[tex]\csc(5\pi+x)=\csc(3\pi+x)=\csc(\pi+x)=\boxed{-\csc x}[/tex]