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Author: Tinku Tara

Find-1-tan1-1-tan2-1-tan44-1-tan46-1-tan47-1-tan89-

Question Number 216836 by hardmath last updated on 22/Feb/25 $$\mathrm{Find}: \\ $$$$\frac{\left(\mathrm{1}\:+\:\mathrm{tan1}°\right)\left(\mathrm{1}\:+\:\mathrm{tan2}°\right)…\left(\mathrm{1}\:+\:\mathrm{tan44}°\right)}{\left(\mathrm{1}−\mathrm{tan46}°\right)\left(\mathrm{1}−\mathrm{tan47}°\right)…\left(\mathrm{1}−\mathrm{tan89}°\right)}\:=\:? \\ $$ Answered by BaliramKumar last updated on 22/Feb/25 $$\mathrm{1} \\ $$ Answered…

f-x-ax-4-bx-3-cx-2-dx-e-f-1-2-f-2-3-f-3-4-f-4-5-f-0-25-Then-f-5-Help-me-please-

Question Number 216820 by Ismoiljon_008 last updated on 22/Feb/25 $$ \\ $$$$\:\:\:{f}\left({x}\right)\:=\:{ax}^{\mathrm{4}} \:+\:{bx}^{\mathrm{3}} \:+\:{cx}^{\mathrm{2}} \:+\:{dx}\:+\:{e} \\ $$$$\:\:\:{f}\left(\mathrm{1}\right)\:=\:\mathrm{2} \\ $$$$\:\:\:{f}\left(\mathrm{2}\right)\:=\:\mathrm{3} \\ $$$$\:\:\:{f}\left(\mathrm{3}\right)\:=\:\mathrm{4} \\ $$$$\:\:\:{f}\left(\mathrm{4}\right)\:=\:\mathrm{5}\: \\ $$$$\:\:\:{f}\left(\mathrm{0}\right)\:=\:\mathrm{25}…

Prove-0-1-K-x-3-x-dx-1-96pi-3-1-24-3-24-7-24-11-24-

Question Number 216819 by MrGaster last updated on 22/Feb/25 $$\mathrm{Prove}:\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{K}}\left({x}\right)}{\:\sqrt{\mathrm{3}−{x}}}{dx}=\frac{\mathrm{1}}{\mathrm{96}\pi\sqrt{\mathrm{3}}}×\Gamma\left(\frac{\mathrm{1}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{3}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{7}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{11}}{\mathrm{24}}\right) \\ $$ Answered by MrGaster last updated on 24/May/25 $$\boldsymbol{\mathrm{K}}\left({x}\right)=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{d}\theta}{\:\sqrt{\mathrm{1}−{x}\:\mathrm{sin}^{\mathrm{2}} \theta}}…