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Question-71944

Question Number 71944 by aliesam last updated on 22/Oct/19 Answered by mind is power last updated on 23/Oct/19 $$\mathrm{a}=\left\{\left(−\mathrm{1}\right)^{\mathrm{k}} \left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{k}}\right);\mathrm{k}\in\mathrm{Z}\right\} \\ $$$$\mathrm{let}\:\mathrm{a}_{\mathrm{n}} \in\mathrm{a} \\ $$$$\mathrm{a}_{\mathrm{2n}}…

Question-137477

Question Number 137477 by Sandeep11 last updated on 03/Apr/21 Commented by MJS_new last updated on 03/Apr/21 $$\mathrm{well}\:\mathrm{just}\:\mathrm{derivate}\:\mathrm{the}\:\mathrm{answers}\:\mathrm{and}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{right}\:\mathrm{one}?! \\ $$ Answered by soumyasaha last…

Find-the-value-of-cos-1-isin-1-cos-2-isin-2-cos-359-isin-359-

Question Number 137468 by ZiYangLee last updated on 03/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\left(\mathrm{cos}\:\mathrm{1}°+{i}\mathrm{sin}\:\mathrm{1}°\right)\left(\mathrm{cos}\:\mathrm{2}°+{i}\mathrm{sin}\:\mathrm{2}°\right)\ldots\left(\mathrm{cos}\:\mathrm{359}°+{i}\mathrm{sin}\:\mathrm{359}°\right). \\ $$ Answered by mr W last updated on 03/Apr/21 $$={e}^{\frac{\mathrm{1}}{\mathrm{180}}\pi{i}} {e}^{\frac{\mathrm{2}}{\mathrm{180}}\pi{i}} …{e}^{\frac{\mathrm{359}}{\mathrm{180}}\pi{i}}…

Question-137467

Question Number 137467 by SOMEDAVONG last updated on 03/Apr/21 Answered by Ñï= last updated on 03/Apr/21 $${I}=\int\frac{{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} }{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx}=\int\frac{{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} }{{i}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}=\frac{\mathrm{1}}{{i}}\int{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} {d}\left(\mathrm{sin}^{−\mathrm{1}}…