Proving tan(45+x)=cot(45-x) in Degrees

[Miike012]

Homework Statement

Prove: tan( 45 + x) =cot( 45 - x )

Note: the numbers that I am using are in deg.

Working with left side:
tan( 90 - 90 + 45 + x )
=tan(90 - 45 + x)
=tan(90 -(45+x))
=cot(45 +x)
Is my algebra correct?

If so why am I getting pos x and not a neg x?
and if this is true that is kind of weird that tan (90+x) = cot(90+x)

Homework Equations

The Attempt at a Solution

 

[Miike012]

Nevermind... I did not factor out a neg 1 from the x.. I know what I did wrong ..