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The domain of $f(x)=\log_{\tan x}(2\sin x-1)$ is |
$\underset{n∈I}{U}\left(2nπ+\frac{π}{6},\,2nπ+\frac{π}{4}\right)∪\left(2nπ+\frac{π}{6},\,(4n+1)\frac{π}{2}\right)$ $\underset{n∈I}{U}\left(2nπ+\frac{π}{6},\,2nπ+\frac{5π}{6}\right)$ $\underset{n∈I}{U}\left(2nπ,(2n+1)\right)$ none of these |
$\underset{n∈I}{U}\left(2nπ+\frac{π}{6},\,2nπ+\frac{π}{4}\right)∪\left(2nπ+\frac{π}{6},\,(4n+1)\frac{π}{2}\right)$ |
$log_{\tan x} (2\sin x-1)$ is defined only when $2\sin x −1> 0$ and $\tan x > 0$ and $\tan x ≠1$ $⇒x∈\left(2nπ+\frac{π}{6},\,2nπ+\frac{π}{4}\right)∪\left(2nπ+\frac{π}{6},\,(4n+1)\frac{π}{2}\right)$ |
