Question

Cot x sec4x = cot x + 2 tan x + tan3x
Is this equation or identity?

Answer 1

It is an equation:
here is the proof :
The key to this one is that sec^2(x) = 1 + tan^2(x).
So the left side is
cot(x) (1 + tan^2(x)) (1 + tan^2(x))
Expanding this term by term you get
cot(x) + 2 cot(x) tan^2(x) + cot(x) tan^4(x),
but since cot(x) tan(x) = 1, that turns into
cot(x) + 2 tan(x) + tan^3(x),
which is the same as the right side.

Answer 2

The correct answer is:

An equation.

Step-by-step explanation:

An equation is a statement that is true for particular values of the variable. An identity, however, is a statement that is true for any values of the variable.

If we use 60° as x, the left hand side of the equation gives us -1.15. The right hand side gives us 4.04. These are not equal, so this cannot be an identity.