Taylor Expansion of $\cot(x+(π/4))$? what is the Taylor expansion of the function $\cot(x+(π/4))$? Ignore the powers of $x$ which are bigger than $4$.
I think that there should be other easy ways  instead of getting derivatives of $\cot x$ and..... then plugging $x+(π/4)$ ...by the way is there any shortcuts?? 

One alternative is to rewrite $\cot(x+\frac{\pi}{4})$ as $$\frac{\cos(x+\frac{\pi}{4})}{\sin(x+\frac{\pi}{4})}=\frac{\cos x(\frac{\sqrt{2}}{2})-\sin x(\frac{\sqrt{2}}{2})}{\sin x(\frac{\sqrt{2}}{2})-\cos x(\frac{\sqrt{2}}{2})}=\frac{\cos x-\sin x}{\sin x + \cos x},$$ and then multiplying by $\frac{\cos x+\sin x}{\cos x + \sin x}$ to get $$\frac{\cos 2x}{1+\sin 2x}.$$
Then you can divide $\cos 2x=1-2x^2+\frac{2}{3}x^4-\cdots$ 
by 
$1+\sin 2x=1+2x-\frac{4}{3}x^3+\cdots$
