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