solve problem

Question

Verify the identity

 

csc (-1)/cot (t) =  cot (t)/ csc (t+1)

Answer 1

Let t= -1, then the right side = 0, since csc0 = 1/sin0 = 1/0; cot(-1)/1/0 = 0/1 times cot(-1) =0

but the left side = csc(-1)/cot(-1) = 1/cos(-1)/cos(-1)/sin(-1) = sin(-1)/cos^2(-1) which does not =0 whether you consider the angle as -1 radian or -1 degree

It's not a trig identity as written. It just takes one counterexample to disprove a supposed "identity"

possibly you meant some version of the trig identity csc^2(t) - 1 = cot^2(t)

If you cross multiply what you have you'd with t as the angle, you'd have csc^2(t) = cot^2(t) which just needs a -1 to make it the trig identity.