Question Number 191229 by mr W last updated on 22/Apr/23 $${evaluate} \\ $$$${P}_{{n}} =\left({a}+\mathrm{sin}\:\theta\right)\left({a}+\mathrm{sin}\:\frac{\theta}{\mathrm{2}}\right)\left({a}+\mathrm{sin}\:\frac{\theta}{\mathrm{2}^{\mathrm{2}} }\right)…\left({a}+\mathrm{sin}\:\frac{\theta}{\mathrm{2}^{{n}} }\right) \\ $$$${with}\:\mid{a}\mid\leqslant\mathrm{1} \\ $$ Terms of Service Privacy Policy…
Question Number 60155 by Tawa1 last updated on 18/May/19 $$\mathrm{Show}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{cos}\left(\mathrm{x}\right)\:+\:\mathrm{cos}\left(\mathrm{2x}\right)\:+\:…\:+\:\mathrm{cos}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{sin}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}} \\ $$$$\mathrm{By}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$ Answered by Kunal12588 last updated on 18/May/19 $$\:{P}\left({n}\right):\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{cos}\left(\mathrm{x}\right)\:+\:\mathrm{cos}\left(\mathrm{2x}\right)\:+\:…\:+\:\mathrm{cos}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{sin}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}} \\…
Question Number 60054 by bhanukumarb2@gmail.com last updated on 17/May/19 Commented by bhanukumarb2@gmail.com last updated on 17/May/19 $${is}\:{titu}\:{lemma}\:{applicable}\:{here}??{plz}\:{see} \\ $$$${previous}\:{doubts} \\ $$ Answered by tanmay last…
Question Number 191028 by Mingma last updated on 16/Apr/23 Answered by Frix last updated on 16/Apr/23 $$\mathrm{Not}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{but}\:\mathrm{an}\:\mathrm{idea}\:\mathrm{for}\:\mathrm{a}\:\mathrm{proof}: \\ $$$$\left({n}−\mathrm{1}\right){n}\left({n}+\mathrm{1}\right)×{N}={k}^{\mathrm{3}} ;\:{k}\in\mathbb{N} \\ $$$$\mathrm{We}\:\mathrm{know}\:\mathrm{that} \\ $$$$\mathrm{1}.\:\mathrm{gcd}\:\left({n}−\mathrm{1},\:{n}\right)\:=\mathrm{1} \\…
Question Number 191025 by Rupesh123 last updated on 16/Apr/23 Commented by Rasheed.Sindhi last updated on 17/Apr/23 $${n}=\mathrm{8} \\ $$$$\overset{×} {\mathrm{1}},\overset{×} {\mathrm{2}},\mathrm{3},\overset{×} {\mathrm{4}},\mathrm{5},\overset{×} {\mathrm{6}},\mathrm{7} \\ $$$$\:\:\:\:\left(\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{6}\:{are}\:{not}\:{relatively}\:{prime}\right)…
Question Number 190985 by Rupesh123 last updated on 15/Apr/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125314 by peter frank last updated on 10/Dec/20 $$\mathrm{make}\:\mathrm{x}\:\mathrm{the}\:\mathrm{subject} \\ $$$$\mathrm{y}=\mathrm{x}! \\ $$ Commented by john_santu last updated on 10/Dec/20 $${may}\:{be}\:{make}\:{x}\:{as}\:{predicat}\: \\ $$…
Question Number 59763 by ANTARES VY last updated on 14/May/19 $$\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}+\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{2}}−\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}} \\ $$$$\boldsymbol{\mathrm{simplify}}. \\ $$ Answered by Kunal12588 last updated on 14/May/19 $$\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}=\sqrt{\frac{\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{2}}} \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}=\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{2}}}…
Question Number 59562 by shaifalzhob last updated on 11/May/19 $$\left.\mathrm{Derive}\:\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{motion}\:\mathrm{1}\right)\mathrm{Vu}+\mathrm{at} \\ $$ Answered by Forkum Michael Choungong last updated on 11/May/19 $${remeber}\:\:{a}=\frac{\bigtriangleup{v}}{{t}} \\ $$$$\Rightarrow{a}\:=\:\frac{{v}−{u}}{{t}} \\…
Question Number 190618 by mustafazaheen last updated on 07/Apr/23 $$\mathrm{f}\left(\mathrm{x}−\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}\:\:,\mathrm{f}\left(\mathrm{5}\right)=−\mathrm{1} \\ $$$$\mathrm{f}\left(−\mathrm{1}\right)=? \\ $$ Answered by aba last updated on 07/Apr/23 $$\mathrm{f}\left(\mathrm{5}−\mathrm{f}\left(\mathrm{5}\right)\right)=\mathrm{5}\Rightarrow\:\mathrm{f}\left(\mathrm{4}\right)=\mathrm{5} \\ $$$$\mathrm{f}\left(\mathrm{4}−\mathrm{f}\left(\mathrm{4}\right)\right)=\mathrm{4}\Rightarrow\mathrm{f}\left(−\mathrm{1}\right)=\mathrm{4} \\…