Question

cot^5 x = cot x/sec^4 x - 2 sec^2 x +1

Answer 1

I tested for x = 10°
LS = cot^5 10° = 5866.87
RS = 4.27
LS ≠ RS

The way you typed it , the equation is NOT an identity

Answer 2

A good example of why we need to use parentheses.

Noticing that

sec^4 x - 2 sec^2 x +1 is a perfect square, let's try

RS:
cot x/(sec^4 x - 2 sec^2 x +1)
cot x/(sec^2 x - 1)^2
cot x/(tan^2 x)^2
cot x/tan^4 x
cot^5 x
= LS