Can you show me the solutions (possibly step-by-step) of these problems?

1) Calculate the domain of the function:

$\displaystyle \lg{\left( \frac{1+2\cos x}{1 - 2\sin x}\right)}$

2) Calculate the domain of the function:

$\displaystyle \sqrt{\frac{\lg x +1}{\lg x + 3}}$

3) Find the solutions of the inequality:

$\displaystyle \frac{2\times 3^x + 1}{3^{x+1} -1} > 1$

Thank you in advance.