Question Number 147933 by mathdanisur last updated on 24/Jul/21 $${Simplify} \\ $$$$\left(\mathrm{1}+\:\frac{\mathrm{1}}{{cos}\mathrm{2}{x}}\right)\centerdot\left(\mathrm{1}+\frac{\mathrm{1}}{{cos}\mathrm{4}{x}}\right)\centerdot\left(\mathrm{1}+\frac{\mathrm{1}}{{cos}\mathrm{8}{x}}\right)=? \\ $$ Answered by som(math1967) last updated on 24/Jul/21 $$\frac{{tanx}}{{tanx}}\left(\mathrm{1}+\frac{\mathrm{1}+{tan}^{\mathrm{2}} {x}}{\mathrm{1}−{tan}^{\mathrm{2}} {x}}\right)\left(\mathrm{1}+\frac{\mathrm{1}+{tan}^{\mathrm{2}} \mathrm{2}{x}}{\mathrm{1}−{tan}^{\mathrm{2}}…
Question Number 147936 by mathdanisur last updated on 24/Jul/21 $${Solve}\:{the}\:{inequality} \\ $$$$\left(\pi\:-\:\mathrm{3}\right)^{\mathrm{2}\boldsymbol{{sin}}\mathrm{2}\boldsymbol{{x}}} \:\leqslant\:\left(\pi\:-\:\mathrm{3}\right)^{\mathrm{2}} \\ $$ Answered by iloveisrael last updated on 24/Jul/21 $$\Rightarrow\pi−\mathrm{3}\:>\mathrm{1}\:\mathrm{then}\:\mathrm{2sin}\:\mathrm{2x}\:\leqslant\mathrm{2} \\ $$$$\Rightarrow\mathrm{sin}\:\mathrm{2x}\:\leqslant\mathrm{1}\:…
Question Number 147932 by mathdanisur last updated on 24/Jul/21 $${if}\:\:\:\frac{\mathrm{1}−{sin}\mathrm{2}{x}}{\mathrm{1}\:+\:{sin}\mathrm{2}{x}}\:=\:\sqrt{\mathrm{17}\:+\:\mathrm{12}\sqrt{\mathrm{2}}} \\ $$$${find}\:\:\:\mid\frac{{sinx}\:+\:{cosx}}{{cosx}\:-\:{sinx}}\mid\:=\:? \\ $$ Answered by iloveisrael last updated on 24/Jul/21 $$\mid\mathrm{x}\mid=\sqrt{\mathrm{x}^{\mathrm{2}} } \\ $$$$\mid\frac{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}\mid\:=\sqrt{\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{2x}}{\mathrm{1}−\mathrm{sin}\:\mathrm{2x}}}\:…
Question Number 82397 by Power last updated on 21/Feb/20 Commented by Power last updated on 21/Feb/20 $$\mathrm{sir}\:\mathrm{mind}\:\mathrm{is}\:\mathrm{power}\:\:,\:\mathrm{sir}\:\mathrm{W}\:,\:\mathrm{sir}\:\mathrm{john}\:\mathrm{santu}\:\mathrm{pls} \\ $$ Commented by Power last updated on…
Question Number 16840 by Sai dadon. last updated on 27/Jun/17 $$\mathrm{6}/\mathrm{2}\left(\mathrm{2}+\mathrm{1}\right) \\ $$ Commented by RasheedSoomro last updated on 27/Jun/17 $$\mathrm{6}/\mathrm{2}\left(\mathrm{2}+\mathrm{1}\right) \\ $$$$=\mathrm{6}/\left\{\mathrm{2}\left(\mathrm{2}+\mathrm{1}\right)\right\} \\ $$$$=\mathrm{6}/\left(\mathrm{2}×\mathrm{3}\right)…
Question Number 82375 by M±th+et£s last updated on 20/Feb/20 $${if}\:\:{x}+{y}=\mathrm{8}\:\:\:\:\:,,{x},{y}\in\mathbb{R}^{+} \\ $$$${prove}\:{that}\: \\ $$$$\left({x}+\frac{\mathrm{1}}{{y}}\right)^{\mathrm{2}} +\left({y}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} \geqslant\frac{\mathrm{289}}{\mathrm{8}} \\ $$ Answered by MJS last updated on 21/Feb/20…
Question Number 16835 by tawa tawa last updated on 26/Jun/17 Answered by sandy_suhendra last updated on 27/Jun/17 $$\left.\mathrm{1}\right) \\ $$$$\mathrm{5C3}×\mathrm{5C3}×\mathrm{4C2} \\ $$$$=\:\mathrm{10}×\mathrm{10}×\mathrm{6} \\ $$$$=\:\mathrm{600}\:\mathrm{ways} \\…
Question Number 16829 by tawa tawa last updated on 26/Jun/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{6}\left(\mathrm{4}^{\mathrm{x}} \:+\:\mathrm{9}^{\mathrm{x}} \right)\:=\:\left(\mathrm{13}.\mathrm{6}\right)^{\mathrm{x}} \\ $$ Commented by mrW1 last updated on 26/Jun/17 $$\mathrm{please}\:\mathrm{check}\:\mathrm{the}\:\mathrm{question}.…
Question Number 16823 by tawa tawa last updated on 26/Jun/17 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{g}. \\ $$$$\mathrm{6}\left(\mathrm{4}^{\mathrm{x}} \:+\:\mathrm{g}^{\mathrm{x}} \right)\:=\:\mathrm{13}.\mathrm{6}^{\mathrm{x}} \\ $$ Commented by mrW1 last updated on 26/Jun/17 $$\mathrm{x}\neq\mathrm{0}…
Question Number 147893 by mathdanisur last updated on 24/Jul/21 $${x}\:+\:\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{4}\:\:\Rightarrow\:\:{x}\:+\:\mathrm{1}\:-\:\frac{\mathrm{1}}{{x}}\:=\:? \\ $$ Commented by aliibrahim1 last updated on 24/Jul/21 $${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\Rrightarrow\:\:\:\:\:\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} =\mathrm{3}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\mathrm{2}=\mathrm{9}…