The domain of $f(x)=\log_{\tan x}(2\sin x-1)$ is
Answer & explanation
Correct answer: option 1
$log_{\tan x} (2\sin x-1)$ is defined only when
$2\sin x −1> 0$ and $\tan x > 0$ and $\tan x ≠1$
$⇒x∈\left(2nπ+\frac{π}{6},\,2nπ+\frac{π}{4}\right)∪\left(2nπ+\frac{π}{6},\,(4n+1)\frac{π}{2}\right)$