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Show that (sec(x))^2 /(sec(x)+1)(sec(x)-1) can be written as (cosec(x))^2.

( sec²(x))/((sec(x)+1)(sec(x)-1))Then, by the rule of 'difference of two squares', we know that this equals= (sec²(x))/(sec²(x)-1)= (sec²x/tan²x)since 1+tan²(x)=sec²(x), we get sec²(x)-1=tan²(x). By multiplying throughout by cos²(x), we get(sec²x/tan²x)=1/sin²(x)=cosec²(x)as required.

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Show that (sec(x))^2 /(sec(x)+1)(sec(x)-1) can be written as (cosec(x))^2.

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