If $f(\theta)=\frac{1}{2-3 \cos \theta}$, then range of $f(\theta)$ is

$\left(-\infty, \frac{1}{5}\right] \cup[1, \infty)$

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

f(\theta)=\frac{1}{2-3 \cos \theta}

, then range of

f(\theta)

View answer and explanation

Correct option: C

(-\infty,-1] \cup\left(\frac{1}{5}, \infty\right)

Option D (

( -\infty, -1] \cup (\frac{1}{5}, \infty)

) is correct because by analyzing the range of

2-3\cos \theta

, we find the range of

f(\theta)

to be

(-\infty, -1] \cup [\frac{1}{5}, \infty)

excluding 0.

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