Question Number 128645 by john_santu last updated on 09/Jan/21 $$\:\mathrm{If}\:\mathrm{6tan}\:^{\mathrm{2}} \mathrm{x}+\mathrm{tan}\:\mathrm{x}.\mathrm{sec}\:\mathrm{x}\:=\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{where} \\ $$$$\frac{\pi}{\mathrm{2}}<\mathrm{x}<\frac{\mathrm{3}\pi}{\mathrm{2}}\:\mathrm{has}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{x}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{x}_{\mathrm{2}} .\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\left(\mathrm{x}_{\mathrm{1}} +\mathrm{x}_{\mathrm{2}} \right). \\ $$ Answered by liberty…
Question Number 128641 by john_santu last updated on 09/Jan/21 $$\:\mathrm{Given}\:\begin{cases}{\mathrm{A}+\mathrm{B}=\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\mathrm{A}−\mathrm{B}=\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{3}}}\end{cases} \\ $$$$\:\mathrm{then}\:\mathrm{tan}\:\mathrm{A}\:=? \\ $$ Answered by liberty last updated on 09/Jan/21 $$\:\left(\mathrm{1}\right)+\left(\mathrm{2}\right)\:\Rightarrow\:\mathrm{2A}\:=\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\mathrm{tan}\:\mathrm{2A}\:=\:\frac{\mathrm{1}/\mathrm{2}+\mathrm{1}/\mathrm{3}}{\mathrm{1}−\left(\mathrm{1}/\mathrm{2}\right)×\left(\mathrm{1}/\mathrm{3}\right)}\:=\:\mathrm{1} \\…
Question Number 128643 by liberty last updated on 09/Jan/21 $$\:\mathrm{If}\:\mathrm{tan}\:\mathrm{x}+\mathrm{sec}\:\mathrm{x}\:=\:\mathrm{b}\:\mathrm{then}\:\mathrm{cos}\:\mathrm{x}\:=? \\ $$ Commented by john_santu last updated on 09/Jan/21 $$\:\mathrm{tan}\:\mathrm{x}\:=\:\mathrm{b}−\mathrm{sec}\:\mathrm{x}\: \\ $$$$\mathrm{squaring}\:\Rightarrow\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}=\mathrm{b}^{\mathrm{2}} −\mathrm{2bsec}\:\mathrm{x}+\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}…
Question Number 63059 by rajesh4661kumar@gamil.com last updated on 28/Jun/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 63060 by rajesh4661kumar@gamil.com last updated on 28/Jun/19 Answered by Hope last updated on 28/Jun/19 $$\sqrt{\frac{\left(\mathrm{1}+{cos}\theta\right)^{\mathrm{2}} }{{sin}^{\mathrm{2}} \theta}}\: \\ $$$$=\mid\frac{\mathrm{1}+{cos}\theta}{{sin}\theta}\mid \\ $$$$=\frac{\mid\mathrm{1}+{cos}\theta\mid}{\mid{sin}\theta\mid} \\ $$$${when}\:\:\:\pi>\theta>\mathrm{0}\:\:{so}\:{sin}\theta=+{ve}…
Question Number 128582 by john_santu last updated on 08/Jan/21 $$\:\:\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)=? \\ $$ Answered by liberty last updated on 08/Jan/21 $$\:\mathrm{T}\:=\:\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{cot}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cot}\:^{\mathrm{2}}…
Question Number 128546 by mr W last updated on 08/Jan/21 $${find}\:{a}\:{simple}\:{expression}\:{for} \\ $$$${y}=\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:{x}\right) \\ $$$${x}\in\mathbb{R}\:{and}\:{x}\:{in}\:{rad}. \\ $$ Commented by liberty last updated on 08/Jan/21…
Question Number 128361 by DomaPeti last updated on 06/Jan/21 $${f}\left({x}\right)= \\ $$$$\frac{{R}}{\:\sqrt{\mathrm{1}−{M}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({atan}\left({N}\centerdot{sin}\left({x}+{c}\right)\right)\right)}} \\ $$$${g}\left({x}\right)={acos}\left({A}\centerdot{sin}\left({atan}\left({N}\centerdot{sin}\left({x}+{c}\right)\right)\right)+\right. \\ $$$$\left.{B}\centerdot{cos}\left({atan}\left({N}\centerdot{sin}\left({x}+{c}\right)\right)\right)\centerdot{cos}\left({D}−{x}\right)\right) \\ $$$$\int\left({f}\left({x}\right)\centerdot{g}\left({x}\right)'\right)={L}\left({x}\right) \\ $$$${L}\left({x}\right)=? \\ $$$$ \\…
Question Number 128336 by liberty last updated on 06/Jan/21 $$\mathrm{If}\:\:\frac{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}{\mathrm{sec}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}}\:=\:\mathrm{5}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{3cos}\:\mathrm{2x}+\mathrm{1}}{\mathrm{3cos}\:\mathrm{2x}−\mathrm{1}}\:?\: \\ $$ Answered by bramlexs22 last updated on 06/Jan/21 $$\:\Rightarrow\:\frac{\mathrm{sec}\:{x}+\mathrm{tan}\:{x}}{\mathrm{sec}\:{x}−\mathrm{tan}\:{x}}\:=\:\mathrm{5} \\ $$$$\Rightarrow\frac{\mathrm{cos}\:{x}\left(\mathrm{sec}\:{x}+\mathrm{tan}\:{x}\right)}{\mathrm{cos}\:{x}\left(\mathrm{sec}\:{x}−\mathrm{tan}\:{x}\right)}\:=\:\mathrm{5} \\…
Question Number 128333 by liberty last updated on 06/Jan/21 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{tan}\:\mathrm{30}°\mathrm{30}'\:=\:\sqrt{\mathrm{6}}\:+\sqrt{\mathrm{2}}\:−\sqrt{\mathrm{3}}\:−\mathrm{2} \\ $$ Commented by MJS_new last updated on 06/Jan/21 $$\mathrm{not}\:\mathrm{true}?! \\ $$$$\mathrm{tan}\:\left(\mathrm{7}.\mathrm{5}°+\mathrm{180}°×{n}\right)\:=−\mathrm{2}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{3}}+\sqrt{\mathrm{6}} \\ $$ Commented…