The range of fx-1-1-2 cos x is

The correct option is B [ 1, 1/3 ] We know that, 1 ≤ cos x ≤ 1 ⇒ 2 ≤ 2 cos x ≤ 2 ⇒ 1 2 ≤ 1 2 cos x ≤ 1+2 ⇒ 1 ≤ 1 2 cos x ≤ 3 ⇒ 1 ≤1/1 2 lcos x≤1/3 ...

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Standard XII

Mathematics

Range of Trigonometric Expressions

The range of ...

Question

The range of $f (x) = \frac{1}{1 - 2 c o s x}$ is

$[\frac{1}{3}, 1]$

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$[- 1, \frac{1}{3}]$

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$[- \infty, - 1] \cup [\frac{1}{3}, \infty]$

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$[\frac{- 1}{3}, 1]$

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Solution

The correct option is B
$[- 1, \frac{1}{3}]$

We know that, $- 1 \leq - c o s x \leq 1$ $\Rightarrow - 2 \leq - 2 c o s x \leq 2 \Rightarrow 1 - 2 \leq 1 - 2 c o s x \leq 1 + 2 \Rightarrow - 1 \leq 1 - 2 c o s x \leq 3 \Rightarrow - 1 \leq \frac{1}{1 - 2 l c o s x} \leq \frac{1}{3} \Rightarrow - 1 \leq f (x) \leq \frac{1}{3} ∴ Range of f = [- 1, \frac{1}{3}]$

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The range of f(x)=11−2 cos x is

The correct option is B [−1,13] We know that, −1≤−cos x≤1 ⇒−2≤−2 cos x≤2⇒1−2≤1−2 cos x≤1+2⇒−1≤1−2 cos x≤3⇒−1≤11−2 lcos x≤13⇒−1≤f(x)≤13∴ Range of f=[−1,13]

The range of $f (x) = \frac{1}{1 - 2 c o s x}$ is