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（江苏省南京市、盐城市 2023 届高三下学期一模数学试题）已知 f ( θ ) = cos 4 θ + cos 3 θ f\left( \theta \right) = \cos {4\theta } + \cos {3\theta } f ( θ ) = cos 4 θ + cos 3 θ θ 1 , θ 2 , θ 3 {\theta }_{1},{\theta }_{2},{\theta }_{3} θ 1 , θ 2 , θ 3 f ( θ ) f\left( \theta \right) f ( θ ) ( 0 , π ) \left( {0,\pi }\right) ( 0 , π ) π 7 ∈ { θ 1 , θ 2 , θ 3 } \frac{\pi }{7} \in \left\{ {{\theta }_{1},{\theta }_{2},{\theta }_{3}}\right\} 7 π ∈ { θ 1 , θ 2 , θ 3 } θ 1 + θ 2 + θ 3 = π {\theta }_{1} + {\theta }_{2} + {\theta }_{3} = \pi θ 1 + θ 2 + θ 3 = π cos θ 1 cos θ 2 cos θ 3 = − 1 8 \cos {{\theta }_{1}}\cos {{\theta }_{2}}\cos {{\theta }_{3}} = - \frac{1}{8} cos θ 1 cos θ 2 cos θ 3 = − 8 1 cos θ 1 + cos θ 2 + cos θ 3 = 1 2 \cos {{\theta }_{1}} + \cos {{\theta }_{2}} + \cos {{\theta }_{3}} = \frac{1}{2} cos θ 1 + cos θ 2 + cos θ 3 = 2 1
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