Help solving disequality and functions domain

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.

Re: Help solving disequality and functions domain

Do you know what "domain" means? Is so what do you know about the domains of the logarithm and square root functions?

Do you know what happens if you mutliply both sides of an inequality by a negative number? Do you know the "laws of exponents".