Question Number 215679 by BaliramKumar last updated on 14/Jan/25 Answered by MATHEMATICSAM last updated on 14/Jan/25 $$\mathrm{sec}^{\mathrm{2}} \theta\:=\:\frac{\mathrm{4}{xy}}{\left({x}\:+\:{y}\right)^{\mathrm{2}} } \\ $$$$\Rightarrow\:\mathrm{cos}^{\mathrm{2}} \theta\:=\:\frac{\left({x}\:+\:{y}\right)^{\mathrm{2}} }{\mathrm{4}{xy}} \\ $$$$\left({x}\:−\:{y}\right)^{\mathrm{2}}…
Question Number 215640 by BaliramKumar last updated on 12/Jan/25 $${If}\:\:\mathrm{2025}^{{sin}^{\mathrm{2}} {x}} \:−\:\mathrm{2025}^{{cos}^{\mathrm{2}} {x}} \:=\:\sqrt{\mathrm{2025}} \\ $$$${then}\:\mathrm{2025}^{{cos}\mathrm{2}{x}} \:+\:\frac{\mathrm{1}}{\mathrm{2025}^{{cos}\mathrm{2}{x}} }\:=\:? \\ $$ Answered by Frix last updated…
Question Number 215473 by alephnull last updated on 08/Jan/25 $${Solve}\:{for}\:{x} \\ $$$$ \\ $$$$\mathrm{2}{sin}^{\mathrm{2}} {x}+\mathrm{3}{sin}\left({x}\right)+\mathrm{1}=\mathrm{0}\:{for}\:\mathrm{0}\:\leqslant\:{x} \\ $$ Answered by Rasheed.Sindhi last updated on 08/Jan/25 $$\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 215349 by mnjuly1970 last updated on 03/Jan/25 $$ \\ $$$$\:\:\:\:{Find}\:{the}\:{type}\:{of}\:{triangle} \\ $$$$\:\:\:\:{such}\:{that}\:{the}\:{following} \\ $$$$\:\:\:\:\:{relationship}\:{holds}\:{between}\: \\ $$$${its}\:{angles}. \\ $$$$\:\:\:\:\:\: \\ $$$$\:{tan}\:\left({B}\right){tan}\left({C}\right)=\:{tan}^{\mathrm{2}} \left(\frac{{B}+{C}}{\mathrm{2}}\:\right)\:\:\:\:\blacksquare \\ $$$$…
Question Number 215277 by efronzo1 last updated on 02/Jan/25 $$\:\:\:\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)\:=\:\frac{\mathrm{5}}{\mathrm{4}} \\ $$$$\:\:\:\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}−\mathrm{sin}\:\mathrm{x}\right)\:=\:? \\ $$ Answered by MrGaster last updated on 02/Jan/25 $$\underset{\mathrm{Commutative}\:\mathrm{law}\:\mathrm{of}\:\mathrm{multiplication}} {\underbrace{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\centerdot\left(\mathrm{1}−\mathrm{cos}\:{x}\right)\left(\mathrm{1}−\mathrm{sin}\:{x}\right)}}=\left(\frac{\mathrm{5}}{\mathrm{4}}\right)\left(\mathrm{1}−\mathrm{cos}\:{x}\right)\left(\mathrm{1}−\mathrm{sin}\:{x}\right) \\ $$$$\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}}…
Question Number 215017 by Hery03 last updated on 25/Dec/24 $${R}\acute {{e}soudre}\:{dans}\:\mathbb{C}\:{l}'\acute {{e}quation}\:: \\ $$$${sin}\left({z}\right)\:=\:\mathrm{2}. \\ $$ Answered by MrGaster last updated on 25/Dec/24 $${z}=−{i}\:\mathrm{ln}\left(\underset{\mathrm{simplify}} {\underbrace{\sqrt{\mathrm{1}−\mathrm{2}^{\mathrm{2}}…
Question Number 214479 by Frangg last updated on 09/Dec/24 Answered by mehdee7396 last updated on 10/Dec/24 $$\frac{\mathrm{5}{x}−\mathrm{6}}{\mathrm{3}{x}}=\frac{\mathrm{26}}{\mathrm{18}}=\frac{\mathrm{13}}{\mathrm{9}} \\ $$$$\mathrm{45}{x}−\mathrm{54}=\mathrm{39}{x} \\ $$$$\mathrm{6}{x}=\mathrm{54}\Rightarrow{x}=\mathrm{9} \\ $$$$ \\ $$$$…
Question Number 214176 by a.lgnaoui last updated on 30/Nov/24 $$\mathrm{find}\:\mathrm{the}\:\mathrm{vslue}\:\mathrm{of}\:\boldsymbol{\mathrm{R}}\left(\mathrm{radius}\:\boldsymbol{\mathrm{o}}\mathrm{f}\:\mathrm{circle}\:\mathrm{betwen}\:\mathrm{two}\:\right. \\ $$$$\:\mathrm{diagrame}\:\mathrm{curves}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\mathrm{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)\:\mathrm{as}\:\mathrm{showen}. \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{use}\:\mathrm{the}\:\mathrm{programer}\:\mathrm{calculator}. \\ $$ Commented by a.lgnaoui last updated on 30/Nov/24 Commented by…
Question Number 214065 by a.lgnaoui last updated on 28/Nov/24 $$\boldsymbol{{Exercice}}\:\boldsymbol{{pratique}}: \\ $$$$\mathrm{determiner}\:\mathrm{Volume}\:\mathrm{de}\:\mathrm{la}\:\mathrm{forme} \\ $$$$\mathrm{AMBN}\::\mathrm{est}\:\mathrm{dans}\:\mathrm{un}\:\mathrm{plan}\:\mathrm{horisontale} \\ $$$$\mathrm{ci}−\mathrm{dessous}.\left(\mathrm{OI}=\mathrm{12}\right) \\ $$$$\left(\mathrm{ACB}\right)\:\mathrm{assimile}\:\mathrm{a}\:\mathrm{une}\:\mathrm{chainette} \\ $$ Commented by a.lgnaoui last updated…
Question Number 213887 by efronzo1 last updated on 20/Nov/24 $$\:\:\:\mathrm{Find}\:\mathrm{amplitude},\:\mathrm{period},\:\mathrm{maximum}\: \\ $$$$\:\:\mathrm{and}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{for}\:\mathrm{function} \\ $$$$\:\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{6}\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{5}}\mathrm{x}\right)−\mathrm{8}\: \\ $$ Answered by alephnull last updated on 08/Jan/25 $${amplitude}={none} \\…