can someone please show me how to verify this identity?

Question

(sec x/csc x minus cot x) minus (sec x/csc x + cot x)= 2 csc x

Answer 1

Is it

(sec x/(csc x - cot x) - (sec x/(csc x + cot x))= 2 csc x or
sec x/csc x - cot x - sec x/csc x + cot x= 2 csc x

The way you typed it, according to order of operation, it would be that last one, but that is not an identity.

so
(sec x/(csc x - cot x) - (sec x/(csc x + cot x))= 2 csc x

LS = (secxcscx + secxcotx - secxcscx + secxcotx)/(csc^2x - cot^2x)
= 2secxcotx/(csc^2x - (csc^2x - 1))
= 2(1/cosx)(cosx/sinx)
= 2/sinx
= 2cscx
= RS

Answer 2

Need some help with this: find all solutions of cot^2 x=3 in the interval [0,2pi)

Answer 3

Verify the Identity for (1-tanx)^2 = sec^2x-2tanx