Question

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

Answer 1

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

Answer 2

addition property of cos