Question Number 206500 by MATHEMATICSAM last updated on 16/Apr/24 $$\mathrm{If}\:{a}\mathrm{sin}^{\mathrm{2}} \theta\:+\:{b}\mathrm{cos}^{\mathrm{2}} \theta\:=\:{c},\:{b}\mathrm{sin}^{\mathrm{2}} \phi\:+\:{a}\mathrm{cos}^{\mathrm{2}} \phi\:=\:{d} \\ $$$$\mathrm{and}\:{a}\mathrm{tan}\theta\:=\:{b}\mathrm{tan}\phi\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:=\:\frac{\mathrm{1}}{{c}}\:+\:\frac{\mathrm{1}}{{d}}\:. \\ $$ Answered by Berbere last updated…
Question Number 206471 by MATHEMATICSAM last updated on 15/Apr/24 $$\mathrm{If}\:{a}\mathrm{sin}\theta\:=\:{b}\mathrm{cos}\theta\:=\:\frac{\mathrm{2}{c}\mathrm{tan}\theta}{\mathrm{1}\:−\:\mathrm{tan}^{\mathrm{2}} \theta}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\left({a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} \right)^{\mathrm{2}} \:=\:\mathrm{4}{c}^{\mathrm{2}} \left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right). \\ $$ Answered by lepuissantcedricjunior last…
Question Number 206434 by MATHEMATICSAM last updated on 14/Apr/24 $$\mathrm{If}\:\mathrm{tan}^{\mathrm{2}} \theta\:=\:\mathrm{1}\:−\:{x}^{\mathrm{2}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{sec}\theta\:+\:\mathrm{tan}^{\mathrm{3}} \theta\mathrm{cosec}\theta\:=\:\sqrt{\left(\mathrm{2}\:−\:{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:. \\ $$ Answered by TonyCWX08 last updated on…
Question Number 206421 by MATHEMATICSAM last updated on 13/Apr/24 $$\mathrm{If}\:\mathrm{tan}{p}\theta\:=\:{p}\mathrm{tan}\theta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{sin}^{\mathrm{2}} {p}\theta}{\mathrm{sin}^{\mathrm{2}} \theta}\:=\:\frac{{p}^{\mathrm{2}} }{\mathrm{1}\:+\:\left({p}^{\mathrm{2}} \:−\:\mathrm{1}\right)\mathrm{sin}^{\mathrm{2}} \theta}\:.\: \\ $$ Answered by Frix last updated on…
Question Number 206362 by MATHEMATICSAM last updated on 12/Apr/24 $$\mathrm{sin}\frac{\pi}{\mathrm{7}}\:×\:\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{7}}\:×\:\mathrm{sin}\frac{\mathrm{3}\pi}{\mathrm{7}}\:=\:? \\ $$ Answered by Skabetix last updated on 12/Apr/24 $$=\frac{\sqrt{\mathrm{7}}}{\mathrm{8}} \\ $$ Answered by Berbere…
Question Number 206048 by MATHEMATICSAM last updated on 05/Apr/24 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2}^{\mathrm{sin}^{\mathrm{2}} \theta} \:+\:\mathrm{2}^{\mathrm{cos}^{\mathrm{2}} \theta} \:\geqslant\:\mathrm{2}\sqrt{\mathrm{2}}. \\ $$ Answered by A5T last updated on 05/Apr/24 $$\mathrm{2}^{{sin}^{\mathrm{2}} \theta}…
Question Number 205808 by cortano12 last updated on 31/Mar/24 Commented by A5T last updated on 02/Apr/24 $${I}\:{guess}\:{this}\:{is}\:{not}\:{uniquely}\:{defined}.\: \\ $$ Commented by A5T last updated on…
Question Number 205596 by cortano12 last updated on 25/Mar/24 Commented by A5T last updated on 25/Mar/24 $${DE}\:{is}\:{not}\:{uniquely}\:{defined}. \\ $$ Answered by TheHoneyCat last updated on…
Question Number 205535 by cortano12 last updated on 24/Mar/24 Answered by A5T last updated on 24/Mar/24 Commented by A5T last updated on 24/Mar/24 $$\frac{{sin}\mathrm{90}=\mathrm{1}}{{BC}}=\frac{{sin}\left(\mathrm{90}−\theta\right)={cos}\theta}{{AB}}\Rightarrow{AB}={BCcos}\theta \\…
Question Number 205429 by mnjuly1970 last updated on 21/Mar/24 $$ \\ $$$$\:\mathrm{I}{f},\:\:\varphi\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\pi\:−{cos}^{\:−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{4}}\:\right)\right) \\ $$$$ \\ $$$$\:\:\:\Rightarrow\:\mathrm{log}_{\:\mathrm{2}} \left(\:\frac{\:\mathrm{1}+\:{cos}\left(\mathrm{6}\varphi\:\right)}{{cos}^{\mathrm{6}} \left(\varphi\:\right)}\:\right)\:=? \\ $$$$ \\ $$ Answered by…