(A) We know that for any $\theta \in \mathbb{R}$,the range of $\cos \theta$ is $[-1, 1]$.Thus,$-1 \leq \cos (4x - 5) \leq 1$.Multiplying the inequalit

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(A) We know that for any $\theta \in \mathbb{R}$,the range of $\cos \theta$ is $[-1, 1]$.Thus,$-1 \leq \cos (4x - 5) \leq 1$.Multiplying the inequality by $3$,we get:$-3 \leq 3 \cos (4x - 5) \leq 3$.Adding $4$ to all parts of the inequality,we get:$-3 + 4 \leq 3 \cos (4x - 5) + 4 \leq 3 + 4$.$1 \leq 3 \cos (4x - 5) + 4 \leq 7$.Therefore,the expression lies in the interval $[1, 7]$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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For $x \in \mathbb{R}$,the range of $3 \cos (4x - 5) + 4$ lies in the interval:

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A
$[1, 7]$
B
$[4, 7]$
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$[0, 7]$
D
$[2, 7]$

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Trigonometrical Ratios, Functions and Identities

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Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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For $x \in \mathbb{R}$,the range of $3 \cos (4x - 5) + 4$ lies in the interval:

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