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Problem If a , b \mathbf{a}, \mathbf{b} a , b c \mathbf{c} c ∀ θ ∈ R \forall \theta \in \mathbb{R} ∀ θ ∈ R [ a cos θ + b sin θ + c cos 2 θ , a cos ( 2 π 3 + θ ) + b sin ( 2 π 3 + θ ) + c cos 2 ( 2 π 3 + θ ) , a cos ( θ − 2 π 3 ) + b sin ( θ − 2 π 3 ) + c cos 2 ( θ − 2 π 3 ) ] \left[ \mathbf{a} \cos \theta + \mathbf{b} \sin \theta + \mathbf{c} \cos 2\theta, \mathbf{a} \cos\left(\frac{2\pi}{3} + \theta\right) + \mathbf{b} \sin\left(\frac{2\pi}{3} + \theta\right) + \mathbf{c} \cos 2\left(\frac{2\pi}{3} + \theta\right), \mathbf{a} \cos\left(\theta - \frac{2\pi}{3}\right) + \mathbf{b} \sin\left(\theta - \frac{2\pi}{3}\right) + \mathbf{c} \cos 2\left(\theta - \frac{2\pi}{3}\right) \right] [ a cos θ + b sin θ + c cos 2 θ , a cos ( 3 2 π + θ ) + b sin ( 3 2 π + θ ) + c cos 2 ( 3 2 π + θ ) , a cos ( θ − 3 2 π ) + b sin ( θ − 3 2 π ) + c cos 2 ( θ − 3 2 π ) ] [ a b c ] cos θ [\mathbf{a} \mathbf{b} \mathbf{c}] \cos \theta [ abc ] cos θ [ a b c ] cos 2 θ [\mathbf{a} \mathbf{b} \mathbf{c}] \cos 2\theta [ abc ] cos 2 θ [ a b c ] cos 3 θ [\mathbf{a} \mathbf{b} \mathbf{c}] \cos 3\theta [ abc ] cos 3 θ Browse the problem library