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Dec
15
comment Using Demoivre's Theorem prove that $ {\cos5 \theta} = 16{\cos^5 \theta} - 20{\cos^3 \theta} + 5{\cos \theta} $ .
As @G-man has answered you need to expand the LHS of your DeMoivre's identity. $$ \{ cos\theta+\iota sin\theta \}^5$$, perhaps by rewrtiing as $$ \{ \{ cos\theta+\iota sin\theta \}^2 \}^2 \{ cos\theta+\iota sin\theta\} $$.
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