An algebra problem by Sandeep Bhardwaj

Algebra Level 3

\[ \dfrac{ \left( \cos 9x -i \sin 9x \right)^{10} \left( \cos 10x + i \sin 10x \right)^{11} }{\left( \cos 10x +i\sin 10x \right)^{20} \left( \cos 18x -i \sin 18x \right)^{10}}= \, ?\]

Clarification: \(i=\sqrt{-1}\).

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