Question Number 21889 by ajfour last updated on 06/Oct/17 $${If}\:{a},{b},\:{and}\:{A}\:{of}\:{a}\:{triangle}\:\:{are}\: \\ $$$${fixed}\:{and}\:{two}\:{possible}\:{values}\:{of}\:{the}\: \\ $$$${third}\:{side}\:{be}\:{c}_{\mathrm{1}} {and}\:{c}_{\mathrm{2}} {such}\:{that} \\ $$$$\boldsymbol{{c}}_{\mathrm{1}} ^{\mathrm{2}} +\boldsymbol{{c}}_{\mathrm{1}} \boldsymbol{{c}}_{\mathrm{2}} +\boldsymbol{{c}}_{\mathrm{2}} ^{\mathrm{2}} =\boldsymbol{{a}}^{\mathrm{2}} ,\:{then}\:{find}\:{angle}\:{A}.…
Question Number 87424 by Rio Michael last updated on 04/Apr/20 $$\mathrm{prove}\:\mathrm{that}\:\:\:\frac{\mathrm{sin}\:{x}\:−\:\mathrm{2}\:\mathrm{sin}\:{x}\:+\:\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{2sin}\:{x}\:+\:\mathrm{sin}\:\mathrm{3}{x}}\:\equiv\:−\mathrm{tan}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right) \\ $$ Commented by john santu last updated on 04/Apr/20 $$\frac{\mathrm{sin}\:\mathrm{3x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{3x}+\mathrm{3sin}\:\mathrm{x}}\:=\:\frac{\mathrm{2cos}\:\mathrm{2x}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{3sin}\:\mathrm{x}−\mathrm{4sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{3sin}\:\mathrm{x}} \\…
Question Number 87419 by john santu last updated on 04/Apr/20 $$\mathrm{if}\:\mathrm{equation}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{sec}\:\mathrm{x}\:−\mathrm{2tan}\:\mathrm{x}\:−\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{roots}\:\mathrm{x}_{\mathrm{1}} \:\&\:\mathrm{x}_{\mathrm{2}} \:,\:\mathrm{then}\:\mathrm{the}\: \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{x}_{\mathrm{1}} −\mathrm{cos}\:\mathrm{x}_{\mathrm{2}} \:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{4}/\mathrm{5}\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{3}/\mathrm{4}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{4}/\mathrm{3}\: \\ $$$$\left(\mathrm{d}\right)\:\mathrm{3}/\mathrm{2}\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{2} \\ $$…
Question Number 21815 by gopikrishnan005@gmail.com last updated on 04/Oct/17 $${sin}\mathrm{18}^{\mathrm{0}} = \\ $$ Commented by Tinkutara last updated on 04/Oct/17 $$\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}} \\ $$ Commented by…
Question Number 87250 by john santu last updated on 03/Apr/20 $$\sqrt[{\mathrm{3}\:\:}]{\mathrm{cos}\:\frac{\pi}{\mathrm{7}}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{7}}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{7}}}\:=? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152715 by Tawa11 last updated on 31/Aug/21 $$\mathrm{By}\:\mathrm{eliminating}\:\:\theta,\:\:\:\mathrm{show}\:\mathrm{that}\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:\:=\:\:\:−\:\:\:\mathrm{y}^{\mathrm{2}} ,\:\:\:\:\:\: \\ $$$$\mathrm{if}\:\:\:\:\:\mathrm{x}\:\mathrm{sin}^{\mathrm{3}} \theta\:\:\:+\:\:\:\mathrm{y}\:\mathrm{cos}^{\mathrm{3}} \theta\:\:\:\:=\:\:\:\:\mathrm{sin}\theta\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\:\mathrm{x}\:\mathrm{sin}\theta\:\:\:\:−\:\:\:\mathrm{y}\:\mathrm{cos}\theta\:\:\:\:=\:\:\:\:\mathrm{0} \\ $$ Commented by Tawa11 last updated on 02/Sep/21…
Question Number 87065 by Power last updated on 02/Apr/20 Commented by MJS last updated on 02/Apr/20 $$\mathrm{2} \\ $$ Commented by Power last updated on…
Question Number 21453 by Joel577 last updated on 24/Sep/17 $$\mathrm{If}\: \\ $$$$\left(\mathrm{1}\:+\:{n}\right)\mathrm{sin}\:\mathrm{2}\theta\:+\:\left(\mathrm{1}\:−\:{n}\right)\mathrm{cos}\:\mathrm{2}\theta\:=\:\mathrm{1}\:+\:{n} \\ $$$$\mathrm{find}\:\mathrm{tan}\:\mathrm{2}\theta \\ $$ Answered by $@ty@m last updated on 24/Sep/17 $$\left(\mathrm{1}−{n}\right)\mathrm{cos}\:\mathrm{2}\theta=\left(\mathrm{1}+{n}\right)\left(\mathrm{1}−\mathrm{sin}\:\mathrm{2}\theta\right) \\…
Question Number 21431 by Tinkutara last updated on 23/Sep/17 $$\mathrm{In}\:\mathrm{any}\:\Delta{ABC},\:{a}\left({b}\:\mathrm{cos}\:{C}\:−\:{c}\:\mathrm{cos}\:{B}\right)\:= \\ $$ Answered by $@ty@m last updated on 23/Sep/17 $$={ab}\mathrm{cos}\:{C}−{ac}\mathrm{cos}\:{B} \\ $$$$=\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}}−\frac{{c}^{\mathrm{2}}…
Question Number 21429 by Tinkutara last updated on 23/Sep/17 $$\mathrm{In}\:\mathrm{any}\:\Delta{ABC},\:\Sigma{a}^{\mathrm{2}} \left(\mathrm{sin}\:{B}\:−\:\mathrm{sin}\:{C}\right)\:= \\ $$ Answered by $@ty@m last updated on 23/Sep/17 $${We}\:{have} \\ $$$$\frac{{a}}{\mathrm{sin}\:{A}}=\frac{{b}}{\mathrm{sin}\:{B}}=\frac{{c}}{\mathrm{sin}\:{C}}={k},\:{say} \\ $$$$\therefore\Sigma{a}^{\mathrm{2}}…