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Author: Tinku Tara

Given-that-I-n-0-1-x-1-x-n-dx-n-Z-show-that-n-2-I-n-nI-n-1-n-1-

Question Number 127090 by physicstutes last updated on 26/Dec/20 $$\mathrm{Given}\:\mathrm{that}\: \\ $$$$\:\:\mathcal{I}_{{n}} \:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}\left(\mathrm{1}−{x}\right)^{{n}} {dx}\:,\:{n}\:\in\:\mathbb{Z}^{+} \\ $$$$\:\mathrm{show}\:\mathrm{that}\:\:\left({n}+\mathrm{2}\right)\mathcal{I}_{{n}} \:=\:{nI}_{{n}−\mathrm{1}} ,\:{n}\:\geqslant\:\mathrm{1}. \\ $$ Answered by Dwaipayan…

cos36-cos72-

Question Number 192624 by sciencestudentW last updated on 23/May/23 $${cos}\mathrm{36}−{cos}\mathrm{72}=? \\ $$ Answered by som(math1967) last updated on 23/May/23 $$\mathrm{2}{sin}\mathrm{54}{sin}\mathrm{18} \\ $$$$=\mathrm{2}×\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{4}}×\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}} \\ $$$$=\mathrm{2}×\frac{\mathrm{5}−\mathrm{1}}{\mathrm{16}}=\frac{\mathrm{1}}{\mathrm{2}} \\…

x-y-k-x-3y-6-x-2-y-2-min-

Question Number 127088 by MathSh last updated on 26/Dec/20 $$\begin{cases}{{x}+{y}={k}}\\{{x}−\mathrm{3}{y}=\mathrm{6}}\end{cases} \\ $$$$\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)_{{min}} =? \\ $$ Commented by hknkrc46 last updated on 26/Dec/20 $$\checkmark\:\boldsymbol{{x}}\:−\:\mathrm{3}\boldsymbol{{y}}\:=\:\left(\boldsymbol{{x}}\:+\:\boldsymbol{{y}}\right)\:−\:\mathrm{4}\boldsymbol{{y}}\:=\:\boldsymbol{{k}}\:−\:\mathrm{4}\boldsymbol{{y}}\:=\:\mathrm{6}…

cot70-4cos70-

Question Number 192623 by sciencestudentW last updated on 23/May/23 $${cot}\mathrm{70}+\mathrm{4}{cos}\mathrm{70}=? \\ $$ Answered by som(math1967) last updated on 23/May/23 $$\:{tan}\mathrm{20}+\mathrm{4}{sin}\mathrm{20} \\ $$$$=\frac{{sin}\mathrm{20}+\mathrm{4}{sin}\mathrm{20}{cos}\mathrm{20}}{{cos}\mathrm{20}} \\ $$$$=\frac{{sin}\mathrm{20}+\mathrm{2}{sin}\mathrm{40}}{\mathrm{cos}\:\mathrm{20}} \\…

3-2-cos-1-2-2-pi-2-1-4-sin-1-2-2pi-2-pi-2-tan-1-2-pi-

Question Number 192622 by sg74656 last updated on 23/May/23 $$\frac{\mathrm{3}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \sqrt{\frac{\mathrm{2}}{\mathrm{2}+\pi^{\mathrm{2}} }}+\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{2}\sqrt{\mathrm{2}\pi}}{\mathrm{2}+\pi^{\mathrm{2}} }+\mathrm{tan}^{−\mathrm{1}} \frac{\sqrt{\mathrm{2}}}{\pi} \\ $$ Answered by witcher3 last updated on 24/May/23 $$\mathrm{nice}\:\mathrm{one}\:\mathrm{tchek}\:\mathrm{please}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{correct}…