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Category: Trigonometry

f-x-arctan-x-1-2x-1-f-1-x-

Question Number 178743 by mathlove last updated on 21/Oct/22 $${f}\left({x}\right)={arctan}\left(\sqrt{\frac{{x}−\mathrm{1}}{\mathrm{2}{x}+\mathrm{1}}}\right)\:\: \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\ $$ Commented by cortano1 last updated on 21/Oct/22 $$\:\mathrm{tan}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{2x}+\mathrm{1}}} \\ $$$$\:\mathrm{tan}\:^{\mathrm{2}}…

prove-that-2tan-1-1-3-tan-1-1-7-pi-4-

Question Number 113200 by bobhans last updated on 11/Sep/20 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{2tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{7}}\right)=\frac{\pi}{\mathrm{4}} \\ $$ Answered by john santu last updated on 11/Sep/20 $$\left({Q}\right)\:{prove}\:{that}\:\mathrm{2}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{7}}\right)\:=\:\frac{\pi}{\mathrm{4}}.…

Given-the-function-f-cos2-sin-for-0-pi-plot-the-graph-for-intervals-of-pi-6-hence-find-the-value-of-cos2-sin-

Question Number 47586 by Rio Michael last updated on 11/Nov/18 $${Given}\:{the}\:{function}\:{f}\left(\theta\right)=\:{cos}\mathrm{2}\theta\:−\:{sin}\theta.\:\left({for}\:\mathrm{0}°\leqslant\theta\leqslant\pi\right) \\ $$$${plot}\:{the}\:{graph}\:{for}\:\:{intervals}\:{of}\:\frac{\pi}{\mathrm{6}}. \\ $$$${hence}\:{find}\:{the}\:{value}\:{of}\:{cos}\mathrm{2}\theta={sin}\theta. \\ $$ Answered by Joel578 last updated on 12/Nov/18 Commented…

Question-112885

Question Number 112885 by malwan last updated on 10/Sep/20 Commented by malwan last updated on 10/Sep/20 $${P}=? \\ $$$$\left({a}\right)\:\left(−\mathrm{5}\pi/\mathrm{4},\mathrm{2}^{\mathrm{1}/\mathrm{2}} \right) \\ $$$$\left({b}\right)\:\left(−\mathrm{5}\pi/\mathrm{4},\mathrm{2}^{−\mathrm{1}/\mathrm{2}} \right) \\ $$$$\left({c}\right)\:\left(−\mathrm{7}\pi/\mathrm{4},\mathrm{2}^{\mathrm{1}/\mathrm{2}}…

p-sin-77-50-19-cos-27-13-1-VI-2-III-3-II-4-I-In-which-region-of-the-fixed-coordinate-system-is-this-point-located-

Question Number 178388 by mathlove last updated on 16/Oct/22 $$\:{p}\left({sin}^{\mathrm{77}} \frac{\mathrm{50}}{\mathrm{19}},{cos}\frac{\mathrm{27}}{\mathrm{13}}\right) \\ $$$$\left.\mathrm{1}\left.\right)\left.\:\left.{VI}\:\:\:\:\mathrm{2}\right){III}\:\:\:\:\:\mathrm{3}\right){II}\:\:\:\:\:\:\:\mathrm{4}\right){I} \\ $$In which region of the fixed coordinate system is this point…

Question-47150

Question Number 47150 by somil last updated on 05/Nov/18 Commented by maxmathsup by imad last updated on 05/Nov/18 $${we}\:{see}\:{that}\:{cos}\theta\:{must}\:{be}\:\geqslant\mathrm{0}\Rightarrow\theta\:\in\left[−\frac{\pi}{\mathrm{2}},\frac{\pi}{\mathrm{2}}\right]\left[\mathrm{2}\pi\right]\:\:{changement}\:={x}\:={sin}\theta\:{give} \\ $$$$\mathrm{3}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }=\mathrm{2}{x}^{\mathrm{2}} \:\Rightarrow\mathrm{9}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)=\mathrm{4}{x}^{\mathrm{4}} \:\Rightarrow\mathrm{4}{x}^{\mathrm{4}}…

cos-cot-sin-tan-csc-sec-

Question Number 178181 by mathlove last updated on 13/Oct/22 $$\frac{{cos}\alpha\:{cot}\alpha−{sin}\alpha\:{tan}\alpha}{{csc}\alpha\:{sec}\alpha}=? \\ $$ Commented by Adedayo2000 last updated on 13/Oct/22 $${Recall}\:{cot}\alpha=\frac{\mathrm{1}}{{tan}\alpha}=\frac{{cos}\alpha}{{sin}\alpha},\:{csc}\alpha=\frac{\mathrm{1}}{{sin}\alpha},\:{sec}\alpha=\frac{\mathrm{1}}{{cos}\alpha} \\ $$$$=>\frac{\left({cos}\alpha\right)\left(\frac{{cos}\alpha}{{sin}\alpha}\right)−\left({sin}\alpha\right)\left(\frac{{sin}\alpha}{{cos}\alpha}\right)}{\left(\frac{\mathrm{1}}{{sin}\alpha}\right)\left(\frac{\mathrm{1}}{{cos}\alpha}\right)} \\ $$$$=>\frac{\frac{{cos}^{\mathrm{2}} \alpha}{{sin}\alpha}−\frac{{sin}^{\mathrm{2}}…