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Question Number 129496 by zakirullah last updated on 16/Jan/21

Commented by zakirullah last updated on 16/Jan/21

$$\:\:\:\:\left(\mathrm{3}^{\mathrm{2n}+\mathrm{2}} \:−\mathrm{8n}−\mathrm{9}\right)\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{64} \\$$$$\:\:\:\:\:\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{prove} \\$$$$\:\:\:\:\:\:\mathrm{cos}\alpha+\mathrm{cos}\left(\alpha+\beta\right)+\mathrm{cos}\left(\alpha+\mathrm{2}\beta\right)+..........+ \\$$$$\:\:\:\:\:\:\mathrm{cos}\left(\alpha+\left(\mathrm{n}−\mathrm{1}\right)\beta\right)=\:\mathrm{cos}\left(\alpha+\frac{\left(\mathrm{n}−\mathrm{1}\right)\beta}{\mathrm{2}}\right)×\frac{\mathrm{sin}\left(\mathrm{n}\beta/\mathrm{2}\right)}{\mathrm{sin}\left(\beta\mathrm{2}\right)} \\$$

Commented by zakirullah last updated on 16/Jan/21

$$\boldsymbol{{please}}\:\boldsymbol{{need}}\:\boldsymbol{{help}}\upuparrows\downdownarrows \\$$

Commented by abdurehime last updated on 16/Jan/21

$$\mathrm{sir}\:\:\mathrm{how}\:\mathrm{to}\:\mathrm{eliminate}\:\mathrm{the}\:\mathrm{which}\:\mathrm{is}\:\mathrm{written}\:\mathrm{vertically}?\:\mathrm{i}.\mathrm{e}\:\mathrm{tink}\:\mathrm{i}\:\mathrm{iara}.\mathrm{com}????? \\$$

Commented by Tinku Tara last updated on 16/Jan/21

$$\mathrm{Use}\:+\:\mathrm{button}\:\mathrm{to}\:\mathrm{write}\:\mathrm{your}\:\mathrm{question} \\$$$$\mathrm{TINKUTARA}\:\mathrm{mark}\:\mathrm{will}\:\mathrm{not} \\$$$$\mathrm{appear}\:\mathrm{on}\:\mathrm{typed}\:\mathrm{posts}. \\$$$$\mathrm{Removing}\:\mathrm{water}\:\mathrm{mark}\:\mathrm{requires}\:\mathrm{premium}. \\$$

Commented by zakirullah last updated on 16/Jan/21

$$\mathrm{you}\:\mathrm{are}\:\mathrm{the}\:\mathrm{great}\:\mathrm{man}\:\mathrm{sir}? \\$$$$\mathrm{you}\:\mathrm{clear}\:\mathrm{a}\:\mathrm{big}\:\mathrm{problum}. \\$$

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