Question

Verify the identity.

cot ((x - (pi/2)) = -tan x

Answer 1

I don't see this as one of the cofunction formulas.

Answer 2

Try this:\[\cot (x-\frac{ \pi }{ 2 })=\frac{ \cos(x-\frac{ \pi }{ 2 } )}{ \sin(x-\frac{ \pi }{ 2 }) }\]Tyou can use the formulas for the complement now, only I don't know if they are called that way:\[\sin(\theta)=\cos(\frac{ \pi }{ 2 }- \theta)\]and\[\cos(\theta)=\sin(\frac{ \pi }{ 2 }- \theta)\]
Now if you compare these formulas with the ones in the fraction above, you'll see that they do not match completely. Luckily, this results in the minus sign you need on the right hand side of your formula.
Please try to think about this now, I hope I haven't been too cryptic... ;)

Answer 3

cot ((x - (pi/2)) = -tan x
you can write cot as cos /sin
then use pi/2-x

Answer 4

Ok, we had: \[\frac{ \cos(x-\frac{ \pi }{ 2 }) }{ \sin(x-\frac{ \pi }{ 2 } )}=\frac{ \cos(\frac{ \pi }{ 2 }-x) }{ -\sin(\frac{ \pi }{ 2 } -x)}=-\frac{ \sin x }{ \cos x }=-\tan x\]