(D) The expression is of the form $a \cos x + b \sin x + c$,where $a = 3$,$b = 4$,and $c = 5$.The range of $a \cos x + b \sin x$ is $[-\sqrt{a^2 + b^2

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(D) The expression is of the form $a \cos x + b \sin x + c$,where $a = 3$,$b = 4$,and $c = 5$.The range of $a \cos x + b \sin x$ is $[-\sqrt{a^2 + b^2}, \sqrt{a^2 + b^2}]$.Calculating the value: $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.Thus,the minimum value of $3 \cos x + 4 \sin x$ is $-5$.Therefore,the minimum value of $3 \cos x + 4 \sin x + 5$ is $-5 + 5 = 0$.

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

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The minimum value of $3 \cos x + 4 \sin x + 5$ is

A
$5$
B
$9$
C
$7$
D
$0$

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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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The minimum value of $3 \cos x + 4 \sin x + 5$ is

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