Prove that :

LHS

We know that sec (-x) = sec (x) and tan (-x) = -tan (x).

We know that when n is odd, sec → cosec and tan → cot.

= [-cosecx] [cosecx] - [-cotx] [cotx]

= -cosec²x + cot²x

= - [cosec²x – cot²x]

We know that cosec²x – cot²x = 1

= -1

= RHS

Hence proved.