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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