Question

2+cotA=1 homework help

Answer 1

$2+\cot A=1\implies \cot A=-1\implies \tan A=-1$

This happens whenever $A=\dfrac{3\pi}4$ or $A=\dfrac{7\pi}4$. More generally, $\tan A=-1$ whenever you start with one of these angles and add any multiple of $\pi$, so the general solution would be $A=\dfrac{3\pi}4+n\pi$, where $n$ is any integer. (Notice that when $n=1$, you end up with $\dfrac{7\pi}4$.)