Category: Algebra

Question Number 190938 by Shrinava last updated on 14/Apr/23 Answered by Frix last updated on 15/Apr/23 $$\tan 3x-\tan x\tan 11x\tan 13x=0$$$$\mathrm{We}\mathrm{can}\mathrm{transform}\mathrm{this}\mathrm{to}$$$$\sin 28x-\sin 20x+\sin 4x=0$$$$y=4x$$$$\mathrm{sin}\:\mathrm{7}{y}\:−\mathrm{sin}\:\mathrm{5}{y}\:+\mathrm{sin}\:{y}\:=\mathrm{0}…

Question Number 190916 by Abdullahrussell last updated on 14/Apr/23 Commented by Rasheed.Sindhi last updated on 14/Apr/23 $$6A+12B+24C=100$$$$6\mid (6A+12B+24C)\wedge 6\nmid 100$$$$\Rightarrow \nexists integersolution!$$ Terms of…

Question Number 59833 by bhanukumarb2@gmail.com last updated on 15/May/19 Answered by tanmay last updated on 15/May/19 $$e^{i\theta }=cos\theta +isin\theta$$$$e^{-i\theta }=cos\theta -isin\theta$$$${cos}\theta=\frac{{e}^{{i}\theta} +{e}^{−{i}\theta} }{\mathrm{2}}\rightarrow{cosi}=\frac{{e}^{−\mathrm{1}}…

Question Number 190894 by mnjuly1970 last updated on 13/Apr/23 $$$$$$f\left(x\right)=mx+cos\left(x\right),m>1$$$$,f^{-1}\left(3\right)=2f^{-1}\left(2\right)$$$$find:f\left(\frac{1}{m}\right)=?$$ Answered by mehdee42 last updated…

Question Number 190882 by mathlove last updated on 13/Apr/23 Commented by Tinku Tara last updated on 14/Apr/23 $$\mathrm{Where}\mathrm{do}\mathrm{you}\mathrm{find}\mathrm{these}\mathrm{questions}?$$ Commented by mathlove last updated…