Question Number 16359 by Tinkutara last updated on 21/Jun/17 $$\mathrm{In}\:\mathrm{a}\:\Delta{ABC}\:\mathrm{if}\:\frac{{s}\:−\:{a}}{{a}\:−\:{b}}\:=\:\frac{{s}\:−\:{c}}{{b}\:−\:{c}}\:,\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:{r}_{\mathrm{1}} ,\:{r}_{\mathrm{2}} ,\:{r}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}. \\ $$$$\mathrm{Here}\:{r}_{\mathrm{1}} ,\:{r}_{\mathrm{2}} \:\mathrm{and}\:{r}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{exradii} \\ $$$$\mathrm{opposite}\:\mathrm{to}\:\mathrm{angles}\:{A},\:{B}\:\mathrm{and}\:{C}\:\mathrm{respectively}. \\ $$ Answered…
Question Number 16354 by Tinkutara last updated on 21/Jun/17 Answered by myintkhaing last updated on 21/Jun/17 $$\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{bc}}+\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}{ab}}=\mathrm{2}−\frac{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} −{b}^{\mathrm{2}}…
Question Number 81884 by rajesh4661kumar@gmail.com last updated on 16/Feb/20 Commented by mind is power last updated on 16/Feb/20 $${applie} \\ $$$${we}\:{can}\:{find}\:{triangle}\: \\ $$$${withe}\:\:\:{sin}^{−} \:{x},{sin}^{−} {y},{sin}^{−}…
Question Number 16338 by ajfour last updated on 20/Jun/17 Commented by mrW1 last updated on 20/Jun/17 $$\mathrm{x}=\frac{\mathrm{ab}\:\mathrm{sin}\:\left(\theta+\emptyset\right)}{\mathrm{a}\:\mathrm{sin}\:\theta\:+\:\mathrm{b}\:\mathrm{sin}\:\emptyset} \\ $$$$\mathrm{y}=\frac{\mathrm{a}\:\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{2ab}\:\mathrm{cos}\:\left(\theta+\emptyset\right)}\:\mathrm{sin}\:\theta}{\mathrm{a}\:\mathrm{sin}\:\theta+\:\mathrm{b}\:\mathrm{sin}\:\emptyset} \\ $$$$\mathrm{z}=\frac{\mathrm{b}\:\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{2ab}\:\mathrm{cos}\:\left(\theta+\emptyset\right)}\:\mathrm{sin}\:\emptyset}{\mathrm{a}\:\mathrm{sin}\:\theta+\:\mathrm{b}\:\mathrm{sin}\:\emptyset}…
Question Number 16273 by Tinkutara last updated on 20/Jun/17 $$\mathrm{If}\:\mathrm{in}\:\Delta{ABC}\:{r}_{\mathrm{1}} \:=\:{r}_{\mathrm{2}} \:+\:{r}_{\mathrm{3}} \:+\:{r},\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{triangle}\:\mathrm{is}\:\mathrm{right}\:\mathrm{angled}. \\ $$ Commented by mrW1 last updated on 20/Jun/17 $$\mathrm{what}\:\mathrm{is}\:\mathrm{r},\mathrm{r}_{\mathrm{1}}…
Question Number 16269 by Tinkutara last updated on 20/Jun/17 $$\mathrm{2}^{\mathrm{nd}} \:\mathrm{part}\:\mathrm{of}\:\mathrm{Q}.\:\mathrm{16214}:\:\mathrm{Prove}\:\mathrm{that} \\ $$$${r}_{\mathrm{1}} \:=\:{s}\:\mathrm{tan}\:\left(\frac{{A}}{\mathrm{2}}\right),\:{r}_{\mathrm{2}} \:=\:{s}\:\mathrm{tan}\:\left(\frac{{B}}{\mathrm{2}}\right), \\ $$$${r}_{\mathrm{3}} \:=\:{s}\:\mathrm{tan}\:\left(\frac{{C}}{\mathrm{2}}\right). \\ $$ Answered by mrW1 last updated…
Question Number 81794 by Power last updated on 15/Feb/20 Commented by Power last updated on 15/Feb/20 $$\mathrm{prove}\:\mathrm{that}\:\:\:\bigtriangleup\:\:\:\:\: \\ $$ Commented by Power last updated on…
Question Number 81760 by jagoll last updated on 15/Feb/20 $${prove}\: \\ $$$$\mathrm{sin}\:{a}+\mathrm{sin}\:{b}+\mathrm{sin}\:{c}\:=? \\ $$$$\mathrm{4cos}\:\left(\frac{{a}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{b}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{c}}{\mathrm{2}}\right) \\ $$ Commented by jagoll last updated on 15/Feb/20 $${thank}\:{you} \\…
Question Number 16179 by Tinkutara last updated on 24/Jun/17 $$\mathrm{If}\:{a}\:>\:\mathrm{0},\:{b}\:>\:\mathrm{0}\:\mathrm{and}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:{a}\:\mathrm{sin}^{\mathrm{2}} \:\theta\:+\:{b}\:\mathrm{cosec}^{\mathrm{2}} \:\theta\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{a}\:\mathrm{sin}^{\mathrm{2}} \:\theta\:+\:{b}\:\mathrm{cos}^{\mathrm{2}} \:\theta, \\ $$$$\mathrm{then}\:\frac{{a}}{{b}}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\left[\boldsymbol{\mathrm{Answer}}:\:\mathrm{4}\right] \\ $$ Answered by ajfour…
Question Number 16093 by Tinkutara last updated on 17/Jun/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mid\mathrm{sin}\:{x}\mid\:=\:\mathrm{tan}\:{x}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{4}\pi\right]\:\mathrm{is}/\mathrm{are}? \\ $$ Commented by Tinkutara last updated on 17/Jun/17 $$\mathrm{My}\:\mathrm{answer}\:\mathrm{comes}\:\mathrm{out}\:\mathrm{to}\:\mathrm{be}\:\mathrm{5}\:\mathrm{but} \\ $$$$\mathrm{answer}\:\mathrm{in}\:\mathrm{book}\:\mathrm{is}\:\mathrm{6}.\:\mathrm{How}? \\…