# Tag Info

### Solving $\tan ^{-1}(\frac{1-x}{1+x})=\frac{1}{2}\tan ^{-1}(x)$

Thank you to @Robin'sPremiumCoffee for a nice algebraic solution. Now the problem with your original method is that although: $$\frac{1-\tan \theta}{1+\tan \theta} = \tan(\frac \pi 4 -\theta)$$ It is ...
• 861
Accepted

### Prove that is is not possible to define the connective $\land$ in terms of $\lnot$ and ↔

First thing you should notice is that you also get $\top$ and $\bot$ since $a\leftrightarrow a =\top$. Also notice that $(\neg a\leftrightarrow b)\equiv \neg(a\leftrightarrow b)$. We also can restrict ...
• 1,512
Accepted

• 1,303
1 vote

### How to prove that $\int_{-\infty}^{+\infty}\frac{1+x}{1+x^2}dx$ doesn't exist

Alternatively, by definition \int_{-\infty}^{+\infty}\frac{1+x}{1+x^{2}}\, {\rm d}x<+\infty \quad \text{ if and only if}\quad \begin{cases} \int_{-\infty}^{\varepsilon}\frac{1+x}{1+x^{2}}\,{\rm d}...
• 2,321

Only top scored, non community-wiki answers of a minimum length are eligible