Question Number 97658 by Vishal Sharma last updated on 09/Jun/20 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\:+\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{7}}+\mathrm{cos}\:\frac{\mathrm{6}\pi}{\mathrm{7}}\:\:\mathrm{is} \\ $$ Commented by bemath last updated on 09/Jun/20 $${x}=\frac{\mathrm{2}\pi}{\mathrm{7}}\: \\ $$$$\frac{\mathrm{cos}\:{x}+\mathrm{cos}\:\mathrm{2}{x}+\mathrm{cos}\:\mathrm{3}{x}}{\mathrm{2sin}\:{x}}×\:\mathrm{2sin}\:{x} \\ $$$$\frac{\mathrm{sin}\:\mathrm{2}{x}+\mathrm{2sin}{x}\:\mathrm{cos}\:\mathrm{2}{x}+\mathrm{2sin}\:{x}\mathrm{cos}\:\mathrm{3}{x}\:}{\mathrm{2sin}\:{x}}\:=…
Question Number 97657 by Vishal Sharma last updated on 09/Jun/20 $$\mathrm{If}\:\:\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta\:=\:\mathrm{0}\:=\:\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta, \\ $$$$\mathrm{then}\:\:\mathrm{cos}\:\mathrm{2}\alpha+\mathrm{cos}\:\mathrm{2}\beta\:= \\ $$ Commented by bemath last updated on 09/Jun/20 $$\left(\mathrm{1}\right)\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta\:=\:\mathrm{0} \\ $$$$\mathrm{2cos}\:\left(\frac{\alpha+\beta}{\mathrm{2}}\right)\:\mathrm{cos}\:\left(\frac{\alpha−\beta}{\mathrm{2}}\right)\:=\:\mathrm{0}…
Question Number 97656 by Vishal Sharma last updated on 09/Jun/20 $$\mathrm{Maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3}\:\mathrm{cos}\:\theta\:+\:\mathrm{4}\:\mathrm{sin}\:\theta\:\mathrm{is} \\ $$ Commented by bobhans last updated on 09/Jun/20 $$\mathrm{max}\:=\:\mathrm{5} \\ $$$$\mathrm{min}\:=\:−\mathrm{5} \\ $$…
Question Number 31953 by 24444355 last updated on 17/Mar/18 $$\mathrm{If}\:{a},\:{b},\:{c},\:{d}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP},\:\mathrm{then}\:\left({a}^{\mathrm{3}} +{b}^{\mathrm{3}} \right)^{−\mathrm{1}} ,\: \\ $$$$\left({b}^{\mathrm{3}} +{c}^{\mathrm{3}} \right)^{−\mathrm{1}} ,\:\left({c}^{\mathrm{3}} +{a}^{\mathrm{3}} \right)^{−\mathrm{1}} \:\mathrm{are}\:\mathrm{in} \\ $$ Commented by…
Question Number 31952 by 24444355 last updated on 17/Mar/18 $$\mathrm{For}\:\mathrm{a}\:\mathrm{sequence}\:<\:{a}_{{n}} \:>\:\:,\:{a}_{\mathrm{1}} =\:\mathrm{2}\:\mathrm{and}\: \\ $$$$\frac{{a}_{{n}+\mathrm{1}} }{{a}_{{n}} }\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\:.\:\:\mathrm{Then}\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:{a}_{{r}} \:\mathrm{is} \\ $$ Commented by abdo imad…
Question Number 31564 by akhilesh2684894@gmail.com last updated on 10/Mar/18 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{and}\:\:{g}\left({x}\right)\:\mathrm{are}\:\mathrm{two}\:\mathrm{integrable} \\ $$$$\mathrm{functions}\:\mathrm{defined}\:\mathrm{on}\:\left[{a},\:{b}\right],\:\mathrm{then} \\ $$$$\mid\:\underset{{a}} {\overset{{b}} {\int}}\:{f}\left({x}\right)\:{g}\left({x}\right)\:{dx}\:\mid\:\:\:\mathrm{is} \\ $$ Commented by MJS last updated on 10/Mar/18…
Question Number 31538 by akhilesh2684894@gmail.com last updated on 09/Mar/18 $$\mathrm{If}\:{f}\left({x}\right)=\:{a}\:{e}^{\mathrm{2}{x}} +{b}\:{e}^{{x}} +{cx}\:\mathrm{satisfies}\:\mathrm{the} \\ $$$$\mathrm{condition}\:{f}\left(\mathrm{0}\right)=\:−\mathrm{1},\:{f}\:'\left(\mathrm{log}\:\mathrm{2}\right)=\mathrm{31}, \\ $$$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{log}\:\mathrm{4}} {\int}}\left({f}\left({x}\right)−{cx}\right)\:{dx}\:=\:\frac{\mathrm{39}}{\mathrm{2}},\:\mathrm{then} \\ $$ Answered by MJS last updated…
Question Number 96845 by DELETED last updated on 05/Jun/20 $$\mathrm{If}\:\mathrm{sin}^{−\mathrm{1}} \frac{{x}}{\mathrm{5}}\:+\:\mathrm{cosec}^{−\mathrm{1}} \frac{\mathrm{5}}{\mathrm{4}}\:=\:\frac{\pi}{\mathrm{2}},\:\mathrm{then}\:{x}= \\ $$ Answered by Sourav mridha last updated on 05/Jun/20 $$\Rightarrow\mathrm{sin}^{−\mathrm{1}} \left(\frac{\boldsymbol{{x}}}{\mathrm{5}}\right)=\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{4}}{\mathrm{5}}\right)=\mathrm{sin}^{−\mathrm{1}}…
Question Number 31255 by Tip Top last updated on 04/Mar/18 $$\mathrm{2}{n}\:\mathrm{boys}\:\mathrm{are}\:\mathrm{randomly}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{two} \\ $$$$\mathrm{subgroups}\:\mathrm{containing}\:{n}\:\mathrm{boys}\:\mathrm{each}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{two}\:\mathrm{tallest}\:\mathrm{boys}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{different}\:\mathrm{groups}\:\mathrm{is} \\ $$ Answered by MJS last updated on…
Question Number 30939 by paddu1234 last updated on 01/Mar/18 $$\mathrm{If}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\:{r}^{\mathrm{2}} \:,\:\mathrm{then} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{{xy}}{{zr}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{yz}}{{xr}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{xz}}{{yr}}\right)\:= \\ $$ Answered by ajfour last…