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Explanation:
the rule cot(x)=cos(x)/sin(x)
and sec(x)=1/cos(x)
[tex]cot(x)sec(x)=(\frac{cos(x)}{sin(x)} )(\frac{1}{cos(x)} )[/tex]
the cos(x) cancell and you are left with 1/sin(x)
Hope that helps :)