My class is going to have an exam tomorrow, but we can't figure out how to solve such equations.
$$\log_{\ \large tg(x)} \sqrt{\sin(x)^2 - 5/12} < 1 $$
We tried to transform $1$ to $\log_{\ \large tg(x)} tg(x)$ and solve it as
$$\sqrt{\sin(x)^2 - 5/12} < tg(x)$$
But we don't know how to continue. Any help will be greatly appreciated.
Square both sides, replace $\tan x$ with $\dfrac{\sin x}{\cos x}$ , and $\cos^2x$ with $1-\sin^2x$.