Question Number 140378 by benjo_mathlover last updated on 07/May/21 $$\sqrt{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}+\mathrm{4cos}\:^{\mathrm{2}} \mathrm{x}}−\sqrt{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}+\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\mathrm{for}\:\mathrm{x}\in\:\left[\:\mathrm{0},\mathrm{2}\pi\:\right] \\ $$ Commented by john_santu last updated on 07/May/21…
Question Number 140368 by meetbhavsar25 last updated on 06/May/21 Answered by benjo_mathlover last updated on 07/May/21 $$\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{3}+\mathrm{5cos}\:\mathrm{x}}{\mathrm{5}+\mathrm{3cos}\:\mathrm{x}}\right)\:=\:\mathrm{u} \\ $$$$\Rightarrow\frac{\mathrm{3}+\mathrm{5cos}\:\mathrm{x}}{\mathrm{5}+\mathrm{3cos}\:\mathrm{x}}\:=\:\mathrm{cos}\:\mathrm{u} \\ $$$$\Rightarrow\mathrm{3}+\mathrm{5cos}\:\mathrm{x}\:=\:\mathrm{5cos}\:\mathrm{u}+\mathrm{3cos}\:\mathrm{u}\:\mathrm{cos}\:\mathrm{x} \\ $$$$\Rightarrow\left(\mathrm{5}−\mathrm{3cos}\:\mathrm{u}\right)\mathrm{cos}\:\mathrm{x}\:=\:\mathrm{5cos}\:\mathrm{u}−\mathrm{3} \\…
Question Number 140338 by Arzoon last updated on 06/May/21 $${if}\:\theta=\frac{\pi}{\mathrm{2}{n}+\mathrm{1}},\:{n}\geqslant\mathrm{1},\:{n}\in{N}\:,{then}\:{prove}\:{that}: \\ $$$${tan}\theta{tan}\mathrm{2}\theta{tan}\mathrm{3}\theta\centerdot\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:{tan}\left({n}\theta\right)\:=\:\sqrt{\mathrm{2}{n}+\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9211 by tawakalitu last updated on 23/Nov/16 $$\mathrm{If} \\ $$$$\mathrm{sinA}\:+\:\mathrm{sinB}\:=\:\mathrm{a} \\ $$$$\mathrm{tanA}\:+\:\mathrm{tanB}\:=\:\mathrm{b} \\ $$$$\mathrm{secA}\:+\:\mathrm{secB}\:=\:\mathrm{c} \\ $$$$\mathrm{Prove}\:\mathrm{that}, \\ $$$$\mathrm{8bc}\:=\:\mathrm{a}\left[\mathrm{4b}^{\mathrm{2}} \:+\:\left(\mathrm{b}^{\mathrm{2}} \:−\:\mathrm{c}^{\mathrm{2}} \right)\right]^{\mathrm{2}} \\ $$…
Question Number 140192 by meetbhavsar25 last updated on 05/May/21 Answered by mr W last updated on 05/May/21 $${say}\:\mathrm{tan}^{−\mathrm{1}} {x}={t} \\ $$$${x}=\mathrm{tan}\:{t} \\ $$$$\mathrm{cos}\:{t}=\mathrm{tan}\:{t}=\frac{\mathrm{sin}\:{t}}{\mathrm{cos}\:{t}} \\ $$$$\mathrm{cos}^{\mathrm{2}}…
Question Number 140177 by liberty last updated on 05/May/21 $$\:\:\:\mathrm{solution}\:\mathrm{set}\:\mathrm{equation} \\ $$$$\:\:\:\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}\:+\:\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}\:^{\mathrm{2}} \mathrm{2x} \\ $$ Answered by som(math1967) last updated on 05/May/21 $$\left({sin}^{\mathrm{2}}…
Question Number 9085 by tawakalitu last updated on 17/Nov/16 Answered by mrW last updated on 17/Nov/16 $${x}^{\mathrm{2}} +\left(\mathrm{2}\frac{\mathrm{1}}{\mathrm{8}}−{x}\right)^{\mathrm{2}} =\left(\mathrm{1}\frac{\mathrm{5}}{\mathrm{8}}\right)^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} +\left(\frac{\mathrm{17}}{\mathrm{8}}−{x}\right)^{\mathrm{2}} −\left(\frac{\mathrm{13}}{\mathrm{8}}\right)^{\mathrm{2}} =\mathrm{0} \\…
Question Number 140138 by henderson last updated on 04/May/21 Answered by mr W last updated on 04/May/21 Commented by mr W last updated on 04/May/21…
Question Number 8999 by tawakalitu last updated on 11/Nov/16 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74520 by chess1 last updated on 25/Nov/19 Answered by MJS last updated on 26/Nov/19 $$\mathrm{0}\leqslant{x}<\mathrm{2}\pi \\ $$$$\mathrm{tan}\:{x}\:>\mathrm{sin}\:{x} \\ $$$$\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}>\mathrm{sin}\:{x} \\ $$$$\mathrm{case}\:\mathrm{1}:\:\mathrm{sin}\:{x}\:>\mathrm{0}\:\Leftrightarrow\:\mathrm{0}<{x}<\pi \\ $$$$\frac{\mathrm{1}}{\mathrm{cos}\:{x}}>\mathrm{1}\:\Leftrightarrow\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}\vee\frac{\mathrm{3}\pi}{\mathrm{2}}<{x}<\mathrm{2}\pi…