MathematicsHard45×since 2004Q5656Let f(θ)=3(sin4(3π2−θ)+sin4(3π+θ))−2(1−sin22θ)f(\theta ) = 3\left( {{{\sin }^4}\left( {{{3\pi } \over 2} - \theta } \right) + {{\sin }^4}(3\pi + \theta )} \right) - 2(1 - {\sin ^2}2\theta )f(θ)=3(sin4(23π−θ)+sin4(3π+θ))−2(1−sin22θ) and S={θ∈[0,π]:f′(θ)=−32}S = \left\{ {\theta \in [0,\pi ]:f'(\theta ) = - {{\sqrt 3 } \over 2}} \right\}S={θ∈[0,π]:f′(θ)=−23}. If 4β=∑θ∈Sθ4\beta = \sum\limits_{\theta \in S} \theta4β=θ∈S∑θ, then f(β)f(\beta )f(β) is equal toA98\frac{9}{8}89B32\frac{3}{2}23C54\frac{5}{4}45D118\frac{11}{8}811Check answerSkip