MathematicsIf A=cos2π33 sin2π33−sin2π33 cos2π33 then A2017=

If $A = [\begin{array}{l} \cos \frac{2 π}{33} \sin \frac{2 π}{33} \\ - \sin \frac{2 π}{33} \cos \frac{2 π}{33} \end{array}] t h e n A^{2017} =$

$L e t θ = \frac{2 π}{33} \Rightarrow A = [\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}]$

$\Rightarrow A^{2017} = [\begin{matrix} \cos 2017 θ & \sin 2017 θ \\ - \sin 2017 θ & \cos 2017 θ \end{matrix}]$

$2017 θ = (2017) \frac{2 π}{33} = 122 π + \frac{8 π}{33} \Rightarrow \cos (2017 θ) = \cos 4 θ;$

$\sin (2017 θ) = \sin 4 θ$

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