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The period of the function $f(x)=e^{\log (\sin x)}+(\tan x)^3-\operatorname{cosec}(3 x-5)$ is
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$2 \pi$
$f(x) \mathrm{e}^{\log (\sin x)}+(\tan x)^3-\operatorname{cosec}(3 x-5)$
$\begin{aligned} & =\sin x+(\tan x)^3-\operatorname{cosec}(3 x-5) \\ & f(x)=f_1(x)+f_2(x)+f_3(x) \\ & \text { Period of } f(x)=\text { LCM of period of } f_1(x), f_2(x) \& f_3(x) \\ & =\operatorname{LCM}(2 \pi, \pi, 2 \pi)=2 \pi\end{aligned}$
$\begin{aligned} & =\sin x+(\tan x)^3-\operatorname{cosec}(3 x-5) \\ & f(x)=f_1(x)+f_2(x)+f_3(x) \\ & \text { Period of } f(x)=\text { LCM of period of } f_1(x), f_2(x) \& f_3(x) \\ & =\operatorname{LCM}(2 \pi, \pi, 2 \pi)=2 \pi\end{aligned}$
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