Category: Trigonometry

Question Number 48066 by rahul 19 last updated on 18/Nov/18 $$\sqrt{\frac{1}{2}}.\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}.\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}}\dots \dots \mathrm{\infty }=?$$ Commented by MJS last updated on 18/Nov/18 $$=\frac{2}{\pi }$$$$\mathrm{approximated}\mathrm{it}\mathrm{but}\mathrm{I}{\mathrm{can}}^{\prime }\mathrm{t}\mathrm{prove}\mathrm{it}$$…

Question Number 47836 by Aknabob1 last updated on 15/Nov/18 $$prove{cosec}^2\theta -cot\theta cosec\theta =1$$ Answered by $@ty@mlastupdatedon15/Nov/18$$LHS={cosec}^2\theta -cot\theta cosec\theta$$$$={cosec}^{\mathrm{2}} \theta−\frac{\mathrm{cos}\:\theta}{\mathrm{sin}\:\theta}×\frac{\mathrm{1}}{\mathrm{sin}\:\theta}…

Question Number 178780 by Laftex234 last updated on 21/Oct/22 Answered by MJS_new last updated on 21/Oct/22 $$\mathrm{lhs}\mathrm{is}\mathrm{defined}\mathrm{for}-1⩽x⩽1\mathrm{and}\mathrm{the}\mathrm{maximum}$$$$\mathrm{is}\frac{5{\pi }^2}{16}\mathrm{at}x=\pm 1\Rightarrow \mathrm{no}\mathrm{solution}$$ Answered by Spillover…

Question Number 178743 by mathlove last updated on 21/Oct/22 $$f\left(x\right)=arctan\left(\sqrt{\frac{x-1}{2x+1}}\right)$$$$f^{-1}\left(x\right)=?$$ Commented by cortano1 last updated on 21/Oct/22 $$\tan \mathrm{f}\left(\mathrm{x}\right)=\sqrt{\frac{\mathrm{x}-1}{2\mathrm{x}+1}}$$$$\:\mathrm{tan}\:^{\mathrm{2}}…

Question Number 178694 by peter frank last updated on 20/Oct/22 $$\mathrm{Find}\mathrm{the}\mathrm{general}\mathrm{solution}\mathrm{of}$$$$2^{\cos 2\theta }+1=3.2^{-\sin {}^2\theta }$$ Answered by Frix last updated on 20/Oct/22 $$\mathrm{2}^{\mathrm{cos}\:\mathrm{2}\theta}…