Question Number 8402 by rhm last updated on 10/Oct/16 $${Q}.\:\left({cos}^{\mathrm{2}} \mathrm{66}^{\mathrm{0}} −{sin}^{\mathrm{2}} \mathrm{6}^{\mathrm{0}} \right)\left({cos}^{\mathrm{2}} \mathrm{48}^{\mathrm{0}} −{sin}^{\mathrm{2}} \mathrm{12}^{\mathrm{0}} \right) \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{16}} \\ $$ Answered by sandy_suhendra…
Question Number 8401 by rhm last updated on 10/Oct/16 $${Q}\:.\mathrm{1}\:\:\:\mathrm{1}+{cos}^{\mathrm{2}} \mathrm{2}{A}=\mathrm{2}\left({cos}^{\mathrm{4}} \:{A}+{sin}^{\mathrm{4}} \:{A}\right) \\ $$$$\mathrm{2}.\:\:{sin}^{\mathrm{2}} {A}+{sin}^{\mathrm{2}} \left(\mathrm{120}^{\mathrm{0}} +{A}\right)+{sin}^{\mathrm{2}} \left(\mathrm{120}^{\mathrm{0}} −{A}\right) \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$ \\…
Question Number 139474 by mathdanisur last updated on 27/Apr/21 $${let}:\:\:\Omega_{\boldsymbol{{n}}} =\underset{\:\mathrm{0}} {\overset{\:\mathrm{2}\pi} {\int}}{cos}\left({x}\right)\centerdot{cos}\left(\mathrm{2}{x}\right)\centerdot…\centerdot{cos}\left({nx}\right)\:{dx} \\ $$$${for}\:{which}\:{integers}\:{n},\:\mathrm{1}\leqslant{n}\leqslant\mathrm{10},\:{is}\:\Omega_{\boldsymbol{{n}}} \neq\mathrm{0}? \\ $$ Answered by mathmax by abdo last updated…
Question Number 139468 by mathdanisur last updated on 27/Apr/21 $${prove}:\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{9}+\mathrm{4}\sqrt{\mathrm{2}}}}\:=\:\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$ Answered by OlafThorendsen last updated on 27/Apr/21 $${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{9}+\mathrm{4}\sqrt{\mathrm{2}}}} \\ $$$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} }} \\ $$$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right)}…
Question Number 8390 by tawakalitu last updated on 09/Oct/16 Answered by fernandodantas1996 last updated on 12/Oct/16 $$ \\ $$$$\: \\ $$$$\left.\mathrm{i}\right)\:\overset{\rightarrow} {\mathrm{F}}+\overset{\rightarrow} {\mathrm{P}}\:=\:\mathrm{6i}\:+\:\mathrm{4j}\:−\:\mathrm{k}\:\Rightarrow\: \\ $$$$\Rightarrow\:\parallel\overset{\rightarrow}…
Question Number 8389 by tawakalitu last updated on 09/Oct/16 Answered by ridwan balatif last updated on 10/Oct/16 $$\mathrm{velocity}\:\mathrm{of}\:\mathrm{alarm}\:\mathrm{clock}\:\mathrm{before}\:\mathrm{strikes}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{is} \\ $$$$\mathrm{v}=\sqrt{\mathrm{2gh}} \\ $$$$\:\:=\sqrt{\mathrm{2}×\mathrm{10}×\mathrm{15}} \\ $$$$\:\:=\sqrt{\mathrm{300}}\mathrm{m}/\mathrm{s} \\…
Question Number 139457 by mnjuly1970 last updated on 27/Apr/21 $$\:_{} \:\:\: \\ $$$$\:\:\:\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}\right)!}\:=\frac{{e}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{3}\sqrt{{e}}}\:{cos}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right) \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…
Question Number 8387 by arinto27 last updated on 09/Oct/16 Answered by ridwan balatif last updated on 10/Oct/16 $$\mathrm{1}.\mathrm{f}\left(\mathrm{x}\right)=\mathrm{5x}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\mathrm{y}\:\:\:=\mathrm{5x}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\mathrm{x}\:\:\:=\frac{\mathrm{y}−\mathrm{1}}{\mathrm{5}} \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=\frac{\mathrm{x}−\mathrm{1}}{\mathrm{5}}\Leftrightarrow\mathrm{f}^{−\mathrm{1}}…
Question Number 139456 by SOMEDAVONG last updated on 27/Apr/21 $$\mathrm{E}=\mathrm{log}_{\mathrm{a}} \sqrt{\frac{\mathrm{c}}{\mathrm{b}^{\mathrm{log}_{\mathrm{ab}} \mathrm{c}} }}+\mathrm{log}_{\mathrm{b}} \sqrt{\frac{\mathrm{c}}{\mathrm{a}^{\mathrm{log}_{\mathrm{ab}} \mathrm{c}} }} \\ $$ Answered by bemath last updated on 27/Apr/21…
Question Number 73918 by arkanmath7@gmail.com last updated on 16/Nov/19 $${find}\:{the}\:{Re}\left({w}\right)\:{and}\:{Im}\left({w}\right) \\ $$$$ \\ $$$${where}\:{w}\:=\:\left({sin}\:{a}\:+\:{icos}\:{a}\right)^{\left({cos}\:{a}\:+\:{isin}\:{a}\right)} \\ $$ Commented by abdomathmax last updated on 16/Nov/19 $${W}=\left({e}^{{i}\left(\frac{\pi}{\mathrm{2}}−{a}\right)} \right)^{{cosa}\:+{isina}}…