Question Number 211019 by peter frank last updated on 26/Aug/24 Answered by som(math1967) last updated on 26/Aug/24 $$\:{let}\:{x}={sin}\alpha\:\:{y}={sin}\beta \\ $$$$\:{cos}\alpha+{cos}\beta={a}\left({sin}\alpha−{sin}\beta\right) \\ $$$$\Rightarrow\frac{\mathrm{2}{cos}\frac{\alpha+\beta}{\mathrm{2}}{cos}\frac{\alpha−\beta}{\mathrm{2}}}{\mathrm{2}{sin}\frac{\alpha−\beta}{\mathrm{2}}{cos}\frac{\alpha+\beta}{\mathrm{2}}}={a} \\ $$$$\Rightarrow{cot}\frac{\alpha−\beta}{\mathrm{2}}={a} \\…
Question Number 211008 by mnjuly1970 last updated on 26/Aug/24 Commented by Frix last updated on 26/Aug/24 $${y}=\alpha{x}+{p}? \\ $$ Commented by mnjuly1970 last updated on…
Question Number 211043 by MATHEMATICSAM last updated on 26/Aug/24 Answered by Ghisom last updated on 26/Aug/24 $$\left({x}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{6}\left({x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{9}= \\ $$$$=\left({x}−\mathrm{1}\right)^{\mathrm{3}} +\mathrm{5}=\mathrm{2024} \\ $$ Answered…
Question Number 210972 by ujah last updated on 25/Aug/24 Answered by TonyCWX08 last updated on 25/Aug/24 $${a}.\: \\ $$$${n}\left({C}\:{only}\right)\:=\:\mathrm{18}−\mathrm{6}−\mathrm{3}=\mathrm{9} \\ $$$$ \\ $$$${b}. \\ $$$${n}\left({One}\:{subject}\:{only}\right)…
Question Number 210989 by mokys last updated on 25/Aug/24 $${prove}\:{tan}\left(\mathrm{72}^{°} \right)={tan}\left(\mathrm{66}^{°} \right)+{tan}\left(\mathrm{36}^{°} \right)+{tan}\left(\mathrm{6}^{°} \right)\:\: \\ $$ Answered by som(math1967) last updated on 26/Aug/24 $${tan}\mathrm{72}={tan}\left(\mathrm{66}+\mathrm{6}\right) \\…
Question Number 210974 by bns970 last updated on 25/Aug/24 $$\sqrt{\mathrm{25}} \\ $$ Answered by TonyCWX08 last updated on 25/Aug/24 $$\sqrt{\mathrm{25}} \\ $$$$=\pm\mathrm{5} \\ $$ Commented…
Question Number 210991 by Ismoiljon_008 last updated on 25/Aug/24 Commented by Ismoiljon_008 last updated on 25/Aug/24 $$\:\:\:{DC}=\mathrm{5} \\ $$ Commented by Ismoiljon_008 last updated on…
Question Number 210987 by RojaTaniya last updated on 25/Aug/24 Answered by Frix last updated on 25/Aug/24 $${x}^{\mathrm{6}} −\frac{\mathrm{133}}{\mathrm{78}}{x}^{\mathrm{5}} +\frac{\mathrm{133}}{\mathrm{78}}{x}−\mathrm{1}=\mathrm{0} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)\left({x}−\frac{\mathrm{2}}{\mathrm{3}}\right)\left({x}−\frac{\mathrm{3}}{\mathrm{2}}\right)\left({x}^{\mathrm{2}} +\frac{\mathrm{6}}{\mathrm{13}}{x}+\mathrm{1}\right)=\mathrm{0} \\ $$ Terms…
Question Number 210971 by black_mamba234 last updated on 25/Aug/24 Answered by A5T last updated on 25/Aug/24 $$\left.\mathrm{2}\right)\:\mathrm{2}{x}_{\mathrm{1}} +\mathrm{4}{y}_{\mathrm{1}} −\mathrm{2}{z}_{\mathrm{1}} =\mathrm{2}\left({x}_{\mathrm{1}} +{k}\right)+\mathrm{4}{y}_{\mathrm{1}} −\mathrm{2}\left({z}_{\mathrm{1}} +{k}\right) \\ $$$${f}\left({x}_{\mathrm{1}}…
Question Number 210996 by RojaTaniya last updated on 25/Aug/24 Answered by Frix last updated on 26/Aug/24 $$\mathrm{Only}\:\mathrm{true}\:\mathrm{for}\:\mathrm{the}\:\mathrm{real}\:\mathrm{solution}\:>\mathrm{0}: \\ $$$${x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{1}=\mathrm{0} \\ $$$${x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{9}{x}=\mathrm{4}{x}^{\mathrm{2}}…