Simplifying arctan(cot(x)) to Terms of x and Constants

[fatlady1ac]

Hello, I need help trying to simplify the equation below, I believe it should be in terms of x and constants only, no trigonometry.

"Simplify arctan(cot(x)), assuming 0<x<pi/2"

After many attempted solutions and failures, my most recent attempt is below.

let arctan(1/tanx) = u
==> tan u = 1/tanx
==> tan u*tan x = 1

This is really the most I can get up to.

Thanks Dylan.

 

[Robert1986]

Is this associated with a trig substitution you did while solving an integral?

 

[fatlady1ac]

No this not associated with any integration, the whole question that I was given is what is in the quotation marks.

Thanks Dylan.

 

[fatlady1ac]

The solution has been found "(Pi/2) - x", just realized that my many hours or stressing was because 'pi' was not written with a capital 'Pi' and syntax would not recognize it.

Thanks Dylan.

 

[Robert1986]

Draw a right triangle. Put x as one of the angles (but not the right angle.) Now, think of these things:

1) cot = adj/opp
2) tan = opp/adj

Now, let y be the other non-right angle. What is the relationship between x and y? What is the relationship between cotx and tany?

 

[Robert1986]

The solution has been found "(Pi/2) - x", just realized that my many hours or stressing was because 'pi' was not written with a capital 'Pi' and syntax would not recognize it.

Thanks Dylan.

OK good. But do you understand it? Or did you just put it into mathematica or something?

 

[fatlady1ac]

No I did understand it, I substituted 'cot x = tan(Pi/2 -x)' into my equation, which was my first attempt of many.
Thanks anyway for your help,
Dylan.