Question

Verify the identity. Justify each step.
sec0/csc0-cot0 - sec0/csc0+cot0 = 2 csc 0

Answer 1

addition property of cos

Answer 2

Add fractions on left side:-

= sec O(csc O + cot O) - sec O (csc O - cot O)
---------------------------------------------------------- Now csc^ O - cot^2O = 1:-
csc^2 O - cot^2 O

so we get sec O csc O + sec O cot O - sec O csc O + sec O csc O

= 2 sec O cot O

= 2 * 1 * cos O
----- ------- = 2/ sin O = 2 csc O
cos O sin O