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] - [-cot x ] [ cot x ] = -cosec 2 x + cot 2 x = - [cosec 2 x – cot 2 x] We know that cosec 2 x – cot 2 x = 1 = -1 = RHS Hence proved.

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.