Question Number 100491 by bobhans last updated on 27/Jun/20 Answered by bramlex last updated on 27/Jun/20 $${let}\:\mathrm{arccot}\:\frac{\mathrm{1}}{\mathrm{2}}\:=\:{z}\:\Rightarrow\:\mathrm{cot}\:{z}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${let}\:\mathrm{arccot}\:\frac{\mathrm{2}}{\mathrm{3}}\:=\:{w}\:\Rightarrow\mathrm{cot}\:{w}\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\Leftrightarrow\mathrm{tan}\:\left({z}+{w}\right)\:=\:\frac{\mathrm{tan}\:{z}+\mathrm{tan}\:{w}}{\mathrm{1}−\mathrm{tan}\:{z}.\mathrm{tan}\:{w}} \\ $$$$=\:\frac{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{2}}}{\mathrm{1}−\mathrm{2}.\frac{\mathrm{3}}{\mathrm{2}}}\:=\:\frac{\mathrm{7}}{\mathrm{2}−\mathrm{6}}\:=\:−\frac{\mathrm{7}}{\mathrm{4}\:}\:\blacksquare\: \\ $$…
Question Number 166013 by mathlove last updated on 11/Feb/22 Answered by JDamian last updated on 11/Feb/22 $${x}_{{r}} ={e}^{{i}\frac{\pi}{\mathrm{2}^{{r}} }} \\ $$$${x}_{\mathrm{1}} {x}_{\mathrm{2}} {x}_{\mathrm{3}} \centerdot\centerdot\centerdot{x}_{\infty} =\:{e}^{{i}\pi\underset{{r}}…
Question Number 165995 by mathlove last updated on 11/Feb/22 $$\begin{cases}{{sinx}+{siny}=\frac{\mathrm{3}}{\mathrm{2}}}\\{\mathrm{2}^{\mathrm{sin}\:{x}} +\mathrm{2}^{\mathrm{sin}\:{y}} =\mathrm{2}+\sqrt{\mathrm{2}}}\end{cases}\:\:\:\:\:\:\:{faind}\:\:\:{x}=? \\ $$ Answered by alephzero last updated on 11/Feb/22 $$\begin{cases}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{y}\:=\:\frac{\mathrm{3}}{\mathrm{2}}}\\{\mathrm{2}^{\mathrm{sin}\:{x}} +\:\mathrm{2}^{\mathrm{cos}\:{y}} \:=\:\mathrm{2}\:+\:\sqrt{\mathrm{2}}}\end{cases} \\…
Question Number 100436 by Dwaipayan Shikari last updated on 26/Jun/20 $$\alpha=\frac{\mathrm{2}\pi}{\mathrm{7}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{tan}\alpha\mathrm{tan2}\alpha+\mathrm{tan2}\alpha\mathrm{tan4}\alpha+\mathrm{tan}\alpha\mathrm{tan4}\alpha \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34671 by math khazana by abdo last updated on 09/May/18 $${calculste}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:{arctan}\left(\frac{\mathrm{2}}{{n}^{\mathrm{2}} }\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 165737 by amin96 last updated on 07/Feb/22 $$ \\ $$Let alpha is acute angle and cos alpha=3/5 prove that alpha is not r.π…
Question Number 34647 by JOHNMASANJA last updated on 09/May/18 $${if}\:\:\:{xsin}^{\mathrm{3}} \theta\:+\:{ycos}^{\mathrm{3}} \theta={sin}\theta{cos}\theta \\ $$$${and}\:{xsin}\theta\:−{ycos}\theta=\mathrm{0} \\ $$$${prove}\:{that}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} =\mathrm{1} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 34645 by JOHNMASANJA last updated on 09/May/18 $${show}\:{that}\:\mathrm{2}{tan}^{−\mathrm{1}} \mathrm{2}\:+\:{tan}^{−\mathrm{1}} \mathrm{3}= \\ $$$$\Pi\:+{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34646 by JOHNMASANJA last updated on 09/May/18 $${show}\:{that}\:\mathrm{2}{tan}^{−\mathrm{1}} \mathrm{2}\:+\:{tan}^{−\mathrm{1}} \mathrm{3}= \\ $$$$\Pi\:+{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}} \\ $$ Answered by ajfour last updated on 09/May/18 $${let}\:\:\:\:\:\mathrm{2}\theta+\phi=\mathrm{2tan}^{−\mathrm{1}}…
Question Number 100133 by bemath last updated on 25/Jun/20 $$\mathrm{If}\:\mathrm{sin}^{−\mathrm{1}} \theta+\mathrm{sin}^{−\mathrm{1}} \beta=\pi\: \\ $$$$\theta+\beta−\frac{\mathrm{2}}{\theta^{\mathrm{2}} +\beta^{\mathrm{2}} }\:=\:? \\ $$ Answered by smridha last updated on 25/Jun/20…