JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Analyzing +4 | -1

Let

f(\theta)=3\left(\sin ^{4}\left(\frac{3 \pi}{2}-\theta\right)+\sin ^{4}(3 \pi+\theta)\right)-2\left(1-\sin ^{2} 2 \theta\right)

and

S=\left\{\theta \in[0, \pi]: f^{\prime}(\theta)=-\frac{\sqrt{3}}{2}\right\}

. If

4 \beta=\sum_{\theta \in S} \theta

, then

f(\beta)

is equal to

View answer and explanation

Correct option: C

\frac{5}{4}

The correct answer is C (

\frac{5}{4}

). This involves simplifying the trigonometric function, finding its derivative, solving the equation

f'(\theta) = -\frac{\sqrt{3}}{2}

, and then evaluating

f(\beta)

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