Q65 / 160 · TS EAMCET 2023 (14 May Shift 1) · Mathematics

The period of the function $f(x)=e^{\log (\sin x)}+(\tan x)^3-\operatorname{cosec}(3 x-5)$ is

  • A
    $\pi$
  • B
    $\frac{\pi}{2}$
  • Correct answer
    C
    $2 \pi$
  • D
    $\frac{2 \pi}{3}$

Solution

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

Hence, the correct answer is option: 'C'.

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