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MCQMediumJEE Main 2023 · 29 January, Shift 1Trigonometric Equations

Mathematics Question from JEE Main 2023 · 29 January, Shift 1

Let f(θ)=3(sin⁡4(3π2−θ)+sin⁡4(3π+θ))−2(1−sin⁡2(2θ))f(\theta) = 3\left(\sin^4\left(\frac{3\pi}{2} - \theta\right) + \sin^4\left(3\pi + \theta\right)\right) - 2\left(1 - \sin^2(2\theta)\right), and S={θ∈[0,π]:f′(θ)=−32}S = \left\{\theta \in [0, \pi] : f'(\theta) = -\frac{\sqrt{3}}{2}\right\}. If 4β=∑θ∈Sθ4\beta = \sum_{\theta \in S} \theta, then f(β)f(\beta) is equal to:

  • A

    118\frac{11}{8}

  • B

    54\frac{5}{4}

  • C

    98\frac{9}{8}

  • D

    32\frac{3}{2}

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