Remark: we are going to use the following identities:
i) cot(x)=cos(x)/sin(x)
ii) [tex] sin ^{2} x+cos^2 x=1 [/tex],
iii) 1/ (sin x) = csc(x)
x^2+1=cot^2(∅)+1=[cos(∅)/sin(∅)]^2+1 by identity i
=[cos^2(∅)]/[sin^2(∅)]+(sin^2∅)/(sin^2∅)
=[cos^2(∅)+sin^2(∅)]/ [sin^2(∅)]=1/ [sin^2(∅)] by identity ii
=[ 1/ sin(∅)]^2=csc^2(∅) by identity iii
Answer: csc^2(∅)
