Thread: Find the value of cot^-1 given arctan

$\displaystyle a = cot^-^1(x)$ given $\displaystyle tan^-^1(x) = \frac{\pi}{4}$

a = ?

No idea where to start I am guessing $\displaystyle cot^-^1 = \frac{1}{tan^-^1}$ but that is probably wrong. Help.

Edit: also tried

$\displaystyle \frac{1}{tan(a)}=x$

$\displaystyle x = tan (\frac{\pi}{4}) = 1$

$\displaystyle \frac{1}{tan(a)} = 1$

$\displaystyle tan(a) = 1$

$\displaystyle a = tan^-^11$

$\displaystyle a = \frac{\pi}{4}$

Not sure if it's right though. Can someone verify please?

Originally Posted by freestar

$\displaystyle a = cot^-^1(x)$ given $\displaystyle tan^-^1(x) = \frac{\pi}{4}$
a = ?
No idea where to start I am guessing $\displaystyle cot^-^1 = \frac{1}{tan^-^1}$ but that is probably wrong. Help.
Edit: also tried
$\displaystyle \frac{1}{tan(a)}=x$
$\displaystyle x = tan (\frac{\pi}{4}) = 1$
$\displaystyle \frac{1}{tan(a)} = 1$
$\displaystyle tan(a) = 1$
$\displaystyle a = tan^-^11$
$\displaystyle a = \frac{\pi}{4}$
Not sure if it's right though. Can someone verify please?

I really have no idea what any of that means.

But: $\displaystyle \text{arccot}(x)=\text{arccot}(0)-\arctan(x).$