Prove that \(\displaystyle{1}+{m}{\cos{{2}}}\theta+{\left(\begin{array}{c} {m}\\{2}\end{array}\right)}{\cos{{4}}}\theta+\ldots+{\left(\begin{array}{c} {m}\\{r}\end{array}\right)}{\cos{{2}}}{r}\theta+\ldots+{\cos{{2}}}{m}\theta={2}^{{n}}{{\cos}^{{m}}\theta}{\cos{{m}}}\theta\)

ropowiec2gkc

ropowiec2gkc

Answered question

2022-04-02

Prove that
1+mcos2θ+(m2)cos4θ++(mr)cos2rθ++cos2mθ=2ncosmθcosmθ

Answer & Explanation

pautmndu

pautmndu

Beginner2022-04-03Added 10 answers

k=0m(mk)cos(2kθ)=Rek=0m(mk)e2ikθ
=Re(1+e2iθ)m
=Re(2m(eiθ+eiθ2)meimθ)
=2mcosmθcosmθ

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