Verify the identity: tan( x + pi/2) = -cot x

Question

Would I use the cofunction identity to figure this out? If so, how?

Answer 1

First, the problem isn't stated correctly: I believe you mean to say tan(x+pi/2) = -cot(x)

 

My thinking: pi/2 is 90 degrees so when you state (x+pi/2) you are rotating x into another quadrant 90 degrees away.

 

If x is a positive value (in quadrant 1), then rotating x by 90 degrees puts it into either quadrant 2 or quadrant 4.  The sign of the value changes.

 

Since tan = opp/adj. when you rotate by 90 degrees, opp and adj swap so cot = adj/opp.

 

I agree that tan(x+pi/2) = -cot(x)

 

I decided the identity by applying the definitions of tan, pi/2, cot as explained above.