Question Number 28515 by beh.i83417@gmail.com last updated on 26/Jan/18 Answered by mrW2 last updated on 26/Jan/18 $$\mathrm{tan}\:\mathrm{20}−\mathrm{tan}\:\mathrm{40}+\mathrm{tan}\:\mathrm{80} \\ $$$$=\mathrm{tan}\:\mathrm{20}−\mathrm{tan}\:\left(\mathrm{60}−\mathrm{20}\right)+\mathrm{tan}\:\left(\mathrm{60}+\mathrm{20}\right) \\ $$$$=\mathrm{tan}\:\mathrm{20}−\frac{\sqrt{\mathrm{3}}−\mathrm{tan}\:\mathrm{20}}{\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{tan}\:\mathrm{20}}+\frac{\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{20}}{\mathrm{1}−\sqrt{\mathrm{3}}\mathrm{tan}\:\mathrm{20}} \\ $$$$=\mathrm{tan}\:\mathrm{20}+\frac{\mathrm{tan}\:\mathrm{20}−\sqrt{\mathrm{3}}}{\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{tan}\:\mathrm{20}}+\frac{\mathrm{tan}\:\mathrm{20}+\sqrt{\mathrm{3}}}{\mathrm{1}−\sqrt{\mathrm{3}}\mathrm{tan}\:\mathrm{20}} \\ $$$$=\mathrm{tan}\:\mathrm{20}+\frac{\mathrm{8tan}\:\mathrm{20}}{\mathrm{1}−\mathrm{3tan}^{\mathrm{2}}…
Question Number 93952 by oustmuchiya@gmail.com last updated on 16/May/20 $${Express}\:{the}\:{following}\:{as}\:{functions} \\ $$$${of}\:\boldsymbol{{A}}: \\ $$$$\left(\mathrm{i}\right)\:{sec}\left({A}−\frac{\mathrm{3}\pi}{\mathrm{2}}\right)\:\:\left(\mathrm{ii}\right)\:{cosec}\left({A}−\frac{\pi}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{iii}\right)\:{tan}\left({A}−\frac{\mathrm{3}\pi_{} }{\mathrm{2}}\right)\:\:\left(\mathrm{iv}\right)\:{cos}\left(\mathrm{720}°+{A}\right) \\ $$$$\left(\mathrm{v}\right)\:{tan}\:\left({A}+\pi\right) \\ $$ Answered by Kunal12588 last…
Question Number 93940 by seedhamaieng@gmail.com last updated on 16/May/20 Commented by Tony Lin last updated on 16/May/20 $${cos}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{5}}={tan}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}} \\ $$$${tan}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}}+{tan}^{−\mathrm{1}} \frac{\mathrm{2}}{\mathrm{5}} \\…
Question Number 159466 by abdullah_ff last updated on 17/Nov/21 $$\mathrm{if}\:{tanA}\:=\:\frac{{a}}{{b}} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{sinA}\:=\:\pm\:\frac{{a}}{\:\sqrt{{a}^{ } \:+\:{b}^{ } }} \\ $$$$\mathrm{please}\:\mathrm{help}.. \\ $$ Answered by Ar Brandon last…
Question Number 159322 by Ar Brandon last updated on 15/Nov/21 $$\mathrm{P}\left(\mathrm{z}\right)=\left(\mathrm{1}+{i}\sqrt{\mathrm{3}}\right){z}^{\mathrm{2}} −\left(−\mathrm{4}+\mathrm{4}{i}\right){z}+\mathrm{2}{i}\mathrm{cos}\left(\frac{\pi}{\mathrm{5}}\right)−\mathrm{2sin}\left(\frac{\pi}{\mathrm{5}}\right) \\ $$$$\mathrm{Let}\:{S}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{P}\left({z}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Express}\:{S}\:\mathrm{in}\:\mathrm{algebraic}\:\mathrm{form}\:\mathrm{then}\:\mathrm{in}\:\mathrm{exponential}\:\mathrm{form}. \\ $$$$\mathrm{b}.\:\mathrm{Deduce}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{values}\:\mathrm{of}\:\mathrm{cos}\left(\frac{\mathrm{5}\pi}{\mathrm{12}}\right)\:\mathrm{and}\:\mathrm{sin}\left(\frac{\mathrm{5}\pi}{\mathrm{12}}\right). \\ $$ Answered by mindispower last updated…
Question Number 28164 by abdo imad last updated on 21/Jan/18 $${simplify}\: \\ $$$${A}={cos}^{\mathrm{4}} \theta\:+{cos}^{\mathrm{4}} \left(\theta+\frac{\pi}{\mathrm{4}}\right)\:+{cos}^{\mathrm{4}} \left(\theta\:+\frac{\mathrm{2}\pi}{\mathrm{4}}\right)\:+{cos}^{\mathrm{4}} \left(\theta\:+\frac{\mathrm{3}\pi}{\mathrm{4}}\right). \\ $$ Answered by ajfour last updated on…
Question Number 28163 by abdo imad last updated on 21/Jan/18 $${let}\:{give}\:{z}=\:{e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{5}\:}} \:\:\:\:{and}\:\:{a}=\:{z}\:+{z}^{\mathrm{4}} \:\:\:\:,\:\:\:{b}=\:{z}^{\mathrm{2}} +{z}^{\mathrm{3}} \\ $$$${find}\:{a}\:{equation}\:{wich}\:{have}\:{a}\:{and}\:{for}\:{rootsthen}\:{find} \\ $$$${the}\:{values}\:{of}\:{cos}\left(\frac{\mathrm{2}\pi}{\left.\mathrm{5}\right)}\right),\:{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right),{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:,{sin}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:,{cos}\left(\frac{\pi}{\mathrm{5}}\right). \\ $$ Terms of Service Privacy Policy…
Question Number 93689 by oustmuchiya@gmail.com last updated on 14/May/20 $${simply}:\frac{\left({cos}\mathrm{2}\Theta−\boldsymbol{{i}}{sin}\mathrm{2}\Theta\right)^{\mathrm{7}} \left({cos}\mathrm{3}\Theta+\boldsymbol{{i}}{sin}\mathrm{3}\Theta\right)^{−\mathrm{5}} }{\left({cos}\mathrm{4}\Theta+\boldsymbol{{i}}{sin}\mathrm{4}\Theta\right)^{\mathrm{12}} \left({cos}\mathrm{5}\Theta−\boldsymbol{{i}}{sin}\mathrm{5}\Theta\right)^{−\mathrm{6}} } \\ $$ Commented by PRITHWISH SEN 2 last updated on 14/May/20…
Question Number 159146 by tounghoungko last updated on 13/Nov/21 $${Find}\:{the}\:{absolute}\:{extrema}\:{of} \\ $$$${f}\left({x}\right)=\:\mathrm{2}\:\mathrm{csc}\:{x}\:+\:\mathrm{cot}\:{x}\:{on}\:{the}\: \\ $$$${interval}\:\left(\frac{\pi}{\mathrm{2}},\:\frac{\mathrm{3}\pi}{\mathrm{2}}\:\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159121 by physicstutes last updated on 13/Nov/21 $$\mathrm{Consider} \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{2}{x}\:−\mathrm{1}. \\ $$$$\mathrm{Use}\:\mathrm{the}\:\mathrm{intermidiate}\:\mathrm{value}\:\mathrm{theorem}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{Rolle}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{establish}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{f}\left({x}\right)\:=\:\mathrm{0}\:\mathrm{has}\:\mathrm{a}\:\mathrm{unique}\:\mathrm{solution} \\ $$$$\left.\mathrm{denoted}\:{a}_{\mathrm{0}} \in\right]\:\mathrm{0},\mathrm{1}\left[.\:\right. \\ $$ Terms…