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Author: Tinku Tara

n-0-0-n-n-

Question Number 151026 by qaz last updated on 17/Aug/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{0}^{\mathrm{n}} }{\mathrm{n}!}=? \\ $$ Answered by ArielVyny last updated on 17/Aug/21 $${according}\:{to}\:{the}\:\:{definition}\: \\ $$$${e}^{{t}}…

Find-all-angles-between-0-and-360-for-which-8sin-3cos-2-

Question Number 85489 by oustmuchiya@gmail.com last updated on 22/Mar/20 $${Find}\:{all}\:{angles}\:{between}\:\mathrm{0}°\:{and}\:\mathrm{360}°,\:{for}\:{which}\:\mathrm{8}{sin}\theta=\mathrm{3}{cos}^{\mathrm{2}} \theta \\ $$ Commented by Tony Lin last updated on 22/Mar/20 $$\mathrm{8}{sin}\theta=\mathrm{3}\left(\mathrm{1}−{sin}^{\mathrm{2}} \theta\right) \\ $$$$\mathrm{3}{sin}^{\mathrm{2}}…

show-that-1-sec-1-1-sec-1-2cosec-cot-

Question Number 85484 by oustmuchiya@gmail.com last updated on 22/Mar/20 $${show}\:{that}\:\frac{\mathrm{1}}{{sec}\theta+\mathrm{1}}+\frac{\mathrm{1}}{{sec}\theta−\mathrm{1}}\equiv\mathrm{2}{cosec}\theta{cot}\theta \\ $$ Answered by som(math1967) last updated on 18/Apr/20 $$\frac{\mathrm{sec}\:\theta−\mathrm{1}+{sec}\theta+\mathrm{1}}{\left({sec}\theta+\mathrm{1}\right)\left({sec}\theta−\mathrm{1}\right)} \\ $$$$=\frac{\mathrm{2}{sec}\theta}{{sec}^{\mathrm{2}} \theta−\mathrm{1}}=\frac{\mathrm{2}{sec}\theta}{{tan}^{\mathrm{2}} \theta}=\frac{\mathrm{2}{sec}\theta{cos}^{\mathrm{2}} \theta}{{sin}^{\mathrm{2}}…

If-and-are-the-roots-of-equation-x-2-px-q-0-and-2-2-are-roots-of-the-equation-x-2-rx-s-0-show-that-the-equation-x-2-4qx-2q-2-r-0-has-real-roots-

Question Number 19945 by Tinkutara last updated on 18/Aug/17 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} \:+\:{px}\:+\:{q}\:=\:\mathrm{0}\:\mathrm{and}\:\alpha^{\mathrm{2}} ,\:\beta^{\mathrm{2}} \:\mathrm{are}\:\mathrm{roots}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:−\:{rx}\:+\:{s}\:=\:\mathrm{0},\:\mathrm{show} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:−\:\mathrm{4}{qx}\:+\:\mathrm{2}{q}^{\mathrm{2}} \:−\:{r}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{real}\:\mathrm{roots}. \\…

If-log-logx-3log-logx-log-log-logx-27-Find-x-

Question Number 151013 by mathdanisur last updated on 17/Aug/21 $$\mathrm{If}\:\:\mathrm{log}\left(\mathrm{log}\boldsymbol{\mathrm{x}}\right)^{\frac{\mathrm{3}\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{logx}}\right)}{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{logx}}\right)\right)}\:} \:=\:\mathrm{27} \\ $$$$\mathrm{Find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$ Answered by Olaf_Thorendsen last updated on 17/Aug/21 $$\mathrm{log}\left(\mathrm{log}{x}\right)^{\frac{\mathrm{3log}\left(\mathrm{log}{x}\right)}{\mathrm{log}\left(\mathrm{log}\left(\mathrm{log}{x}\right)\right)}} \:=\:\mathrm{27}\:=\:\mathrm{3}^{\mathrm{3}} \\…

A-circle-is-inscribed-in-an-isosceles-trapezium-Prove-that-the-ratio-of-the-area-of-the-circle-to-the-area-of-the-trapezium-is-equal-to-the-ratio-of-the-circum-ference-of-the-circle-to-the-perimete

Question Number 19940 by ajfour last updated on 18/Aug/17 $${A}\:{circle}\:{is}\:{inscribed}\:{in}\:{an} \\ $$$${isosceles}\:{trapezium}.\:{Prove}\:{that} \\ $$$${the}\:{ratio}\:{of}\:{the}\:{area}\:{of}\:{the}\:{circle} \\ $$$${to}\:{the}\:{area}\:{of}\:{the}\:{trapezium}\:{is} \\ $$$${equal}\:{to}\:{the}\:{ratio}\:{of}\:{the}\:{circum}- \\ $$$${ference}\:{of}\:{the}\:{circle}\:{to}\:{the}\: \\ $$$${perimeter}\:{of}\:{the}\:{trapezium}. \\ $$ Commented…