(B) Let $f(x) = 4\sin^2 x + 3\cos^2 x$.Using the identity $\sin^2 x + \cos^2 x = 1$,we can write $\cos^2 x = 1 - \sin^2 x$.Substituting this into the

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(B) Let $f(x) = 4\sin^2 x + 3\cos^2 x$.Using the identity $\sin^2 x + \cos^2 x = 1$,we can write $\cos^2 x = 1 - \sin^2 x$.Substituting this into the expression: $f(x) = 4\sin^2 x + 3(1 - \sin^2 x) = 4\sin^2 x + 3 - 3\sin^2 x = \sin^2 x + 3$.Since the range of $\sin^2 x$ is $[0, 1]$,the maximum value of $f(x)$ occurs when $\sin^2 x = 1$.Therefore,the maximum value is $1 + 3 = 4$.

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

Easy

The maximum value of $4\sin^2 x + 3\cos^2 x$ is

A
$3$
B
$4$
C
$5$
D
$7$

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Trigonometrical Ratios, Functions and Identities

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Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

For all values of $\theta$,the values of $3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)$ lie in the interval :

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In the graph of the function $\sqrt{3} \sin x + \cos x$,the maximum distance of a point from the $x$-axis is:

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In a $\Delta ABC$,the value of $\sin A \cos B \cos C + \sin B \cos C \cos A + \sin C \cos A \cos B$ is

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If $A + B + C = 180^{\circ}$,then $\tan A + \tan B + \tan C = $

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In a $\triangle ABC$,suppose none of the angles are multiples of $\frac{\pi}{2}$,then what is the value of $\cot A \cot B + \cot B \cot C + \cot A \cot C$?

MediumAP EAMCET 2021

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The maximum value of $4\sin^2 x + 3\cos^2 x$ is

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