Question Number 14268 by Tinkutara last updated on 30/May/17 $$\mathrm{If}\:\mathrm{tan}\theta\:+\:\mathrm{tan2}\theta\:=\:\mathrm{tan3}\theta,\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{exhaustive}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{satisfying} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{equation}. \\ $$ Answered by linkelly0615 last updated on 30/May/17 $$\because{tan}\mathrm{3}\theta=\frac{{tan}\theta+{tan}\mathrm{2}\theta}{\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta}={tan}\theta+{tan}\mathrm{2}\theta \\…
Question Number 14269 by myintkhaing last updated on 30/May/17 $${In}\:\Delta{ABC},\:{if}\:{sinA}+{sinB}+{sinC}.={cosA}+{cosB}+{cosC}+\mathrm{1}, \\ $$$${then}\:{prove}\:{that}\:\Delta{ABC}\:{is}\:{a}\:{right}\:{triangle}. \\ $$ Answered by prakash jain last updated on 30/May/17 $$\mathrm{sin}\:\mathrm{A}−\mathrm{cos}\:\mathrm{A}+\mathrm{sin}\:\mathrm{B}−\mathrm{cos}\:\mathrm{B}+\mathrm{sin}\:{C}−\mathrm{cos}\:{C}=\mathrm{1} \\ $$$$\mathrm{cos}\:{A}=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−{A}\right)…
Question Number 14267 by Tinkutara last updated on 30/May/17 $$\mathrm{If}\:\mathrm{sin}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{3sin}{x}\mathrm{cos}{x}\:−\:\mathrm{1}\:=\:\mathrm{0}, \\ $$$$\mathrm{then}\:\mathrm{find}\:{x}. \\ $$ Answered by linkelly0615 last updated on 30/May/17 $${set} \\…
Question Number 145305 by puissant last updated on 04/Jul/21 $$\mathrm{R}\acute {\mathrm{e}soudre}\:\:\:\frac{\frac{\mathrm{8}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)}\:+\:\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}\:+\:\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}\right)}\:=\:\mathrm{cotan}^{\mathrm{2}} \left(\mathrm{x}\right)+\frac{\mathrm{4}}{\mathrm{3}} \\ $$ Commented by imjagoll last updated on 04/Jul/21 $$\mathrm{put}\:\mathrm{u}\:=\:\mathrm{cos}\:^{\mathrm{2}}…
Question Number 79766 by jagoll last updated on 28/Jan/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{x} \\ $$$$\mathrm{2}^{\mathrm{x}} =\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{01}^{\mathrm{o}} \right)\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{02}^{\mathrm{o}} \right) \\ $$$$\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{03}^{\mathrm{o}} \right)…\left(\mathrm{1}+\mathrm{tan}\:\mathrm{44}.\mathrm{99}^{\mathrm{o}} \right) \\ $$ Answered by mr W…
Question Number 14189 by tawa tawa last updated on 29/May/17 $$\mathrm{Solve}:\:\:\:\sqrt{\mathrm{sinx}}\:+\:\sqrt{\mathrm{cosx}}\:=\:\mathrm{1} \\ $$$$\mathrm{x}\:\in\:\mathrm{R} \\ $$ Answered by ajfour last updated on 29/May/17 $${let}\:\sqrt{\mathrm{sin}\:{x}}={u}\:\:{and}\:\sqrt{\mathrm{cos}\:{x}}={v} \\ $$$${this}\:{means}\:\:{u}+{v}=\mathrm{1}\:\:\:\:\:\:\:…\left({i}\right)…
Question Number 14174 by Nayon last updated on 29/May/17 $$\:\:{xtan}\left({cos}^{−\mathrm{1}} {x}\right)={cos}\left({sin}^{−\mathrm{1}} {x}\right) \\ $$$${prove}\:{it}….. \\ $$ Answered by ajfour last updated on 29/May/17 $${let}\:\mathrm{cos}^{−\mathrm{1}} {x}=\theta\:\:\:\Rightarrow\:\:{x}=\mathrm{cos}\:\theta…
Question Number 145208 by imjagoll last updated on 03/Jul/21 $$\:\mathrm{If}\:\mathrm{P}\::\:\mathrm{Q}\:=\:\mathrm{tan}\:\mathrm{2A}\::\:\mathrm{cos}\:\mathrm{A} \\ $$$$\:\:\:\:\:\mathrm{Q}\::\:\mathrm{R}\:=\:\mathrm{cos}\:\mathrm{2A}\::\:\mathrm{sin}\:\mathrm{2A} \\ $$$$\:\:\:\:\:\mathrm{then}\:\mathrm{P}\::\:\mathrm{R}\:=? \\ $$ Answered by EDWIN88 last updated on 03/Jul/21 $$\:\frac{{P}}{{Q}}\:=\:\frac{\mathrm{2sin}\:{A}\:\mathrm{cos}\:{A}}{\mathrm{cos}\:\mathrm{2}{A}\:\mathrm{cos}\:{A}}\:=\:\frac{\mathrm{2sin}\:{A}}{\mathrm{cos}\:\mathrm{2}{A}} \\…
Question Number 14130 by Joel577 last updated on 28/May/17 $$\mathrm{How}\:\mathrm{to}\:\mathrm{find}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{if} \\ $$$$\frac{\mathrm{5}\:−\:\mathrm{cos}\:\mathrm{2}\theta}{\mathrm{sin}\:\theta}\:\:\geqslant\:\mathrm{2}{k}\:\:\:\:\:\:\:\:\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\:\pi \\ $$ Commented by Joel577 last updated on 28/May/17 $$\frac{\mathrm{5}\:−\:\mathrm{cos}\:\mathrm{2}\theta}{\mathrm{sin}\:\theta}\:\geqslant\:\mathrm{2}{k} \\ $$$$\frac{\mathrm{4}\:+\:\mathrm{2sin}^{\mathrm{2}} \:\theta}{\mathrm{sin}\:\theta}\:\geqslant\:\mathrm{2}{k}…
Question Number 14078 by Tinkutara last updated on 27/May/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 27/May/17 $$\mathrm{4}{cos}^{\mathrm{3}} {x}−\mathrm{3}{cosx}−\sqrt{\mathrm{3}}{sinx}.{cosx}+{cos}^{\mathrm{2}} {x}−\frac{\mathrm{1}}{\mathrm{2}}=−\mathrm{2} \\ $$$$\mathrm{8}{cos}^{\mathrm{3}} {x}+\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{2}\sqrt{\mathrm{3}}{sinx}.{cosx}−\mathrm{6}{cosx}+\mathrm{3}=\mathrm{0} \\ $$$${cosx}={t}\Rightarrow…