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Author: Tinku Tara

If-5-x-4-y-4-and-2-x-4-y-10-then-find-x-and-y-

Question Number 62609 by hovea cw last updated on 23/Jun/19 $$\mathrm{If}\:\:\mathrm{5}\mid{x}\mid\:+\:\mathrm{4}\mid{y}\mid\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{2}\mid{x}\mid\:−\:\mathrm{4}\mid{y}\mid\:=\:\mathrm{10}, \\ $$$$\mathrm{then}\:\mathrm{find}\:{x}\:\mathrm{and}\:{y}. \\ $$ Answered by $@ty@m last updated on 23/Jun/19 $${Let}\:\mid{x}\mid={a}\:\&\mid{y}\mid={b} \\ $$$$\mathrm{5}{a}+\mathrm{4}{b}=\mathrm{4}\:\:…

If-2-x-3-y-6-z-then-1-x-1-y-1-z-

Question Number 62591 by hovea cw last updated on 23/Jun/19 $$\mathrm{If}\:\:\mathrm{2}^{{x}} =\:\mathrm{3}^{{y}} =\:\mathrm{6}^{{z}} ,\:\mathrm{then}\:\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{y}}\:+\:\frac{\mathrm{1}}{{z}}\:=\:\_\_\_\_. \\ $$ Commented by mr W last updated on 23/Jun/19 $${could}\:{be}\:{any}\:{value}\:{in}\:\left(−\infty,\infty\right)\:{except}\:{zero}.…

If-tan-1-2-and-tan-1-3-then-the-value-of-is-

Question Number 62388 by hovea cw last updated on 20/Jun/19 $$\mathrm{If}\:\mathrm{tan}\:\theta=\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{tan}\:\phi=\frac{\mathrm{1}}{\mathrm{3}},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\theta\:+\:\phi\:\:\:\mathrm{is} \\ $$ Commented by Tony Lin last updated on 20/Jun/19 $${tan}\left(\theta+\emptyset\right)=\frac{{tan}\theta+{tan}\emptyset}{\mathrm{1}−{tan}\theta{tan}\phi}=\mathrm{1} \\…

Question-193438

Question Number 193438 by Mingma last updated on 14/Jun/23 Answered by qaz last updated on 14/Jun/23 $${log}_{\mathrm{3}} \left(\mathrm{9}{x}−\mathrm{3}\right)=\mathrm{1}+{log}_{\mathrm{3}} \left(\mathrm{3}{x}−\mathrm{1}\right)\:\:\:\:\:,{log}_{\mathrm{3}} \left({x}−\frac{\mathrm{1}}{\mathrm{3}}\right)={log}_{\mathrm{3}} \left(\mathrm{3}{x}−\mathrm{1}\right)−\mathrm{1} \\ $$$${log}_{\mathrm{3}} \left(\mathrm{3}{x}−\mathrm{1}\right)={y} \\…

when-tan-2-1-a-then-find-cos-from-the-a-

Question Number 193423 by mustafazaheen last updated on 13/Jun/23 $$\mathrm{when}\:\:\:\mathrm{tan}\frac{\theta}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{a}} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{cos}\theta=?\:\mathrm{from}\:\mathrm{the}\:\mathrm{a} \\ $$ Answered by AST last updated on 13/Jun/23 $${tan}\left(\frac{\theta}{\mathrm{2}}+\frac{\theta}{\mathrm{2}}\right)=\frac{\mathrm{2}{tan}\left(\frac{\theta}{\mathrm{2}}\right)}{\mathrm{1}−{tan}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right)}\Rightarrow{tan}\left(\theta\right)=\frac{\mathrm{2}{a}}{{a}^{\mathrm{2}} −\mathrm{1}} \\…