Reference Triangle Issue - Trig Evaluate $\cos(2\cot^{-1}(32/49))$
What I did for this problem was:


*

*Turn $\cot$ into $\tan(49/32)$

*And I am not sure what I do with the $2*$


I tried multiplying $49$ by $2$ and plugging the values into a reference triangle. 
After I had all three sides I just found the $\cos$ of the triangle and used that as the answer but it was incorrect. I also knew i couldn't use any of the double angle formulas because the two is in front of the identity. 
The cot is inverse
Where did I go wrong?

Use Are $\mathrm{arccot}(x)$ and $\arctan(1/x)$ the same function?
Now if $\tan^{-1}x=y,\tan y=x$
$$\cos\left(2\tan^{-1}x\right)=\cos2y=\dfrac{1-\tan^2y}{1+\tan^2y}=?$$
