Menu Close

Author: Tinku Tara

2cos-pi-13-cos-9pi-13-cos-3pi-13-cos-5pi-13-0-

Question Number 21259 by oyshi last updated on 17/Sep/17 $$\mathrm{2cos}\:\frac{\pi}{\mathrm{13}}\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{13}}+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{13}}+\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{13}}=\mathrm{0} \\ $$ Answered by myintkhaing last updated on 18/Sep/17 $$\mathrm{L}.\mathrm{H}.\mathrm{S}=\mathrm{cos}\:\frac{\mathrm{10}\pi}{\mathrm{13}}\:+\mathrm{cos}\:\frac{\mathrm{8}\pi}{\mathrm{13}}\:+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{13}}\:+\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{13}} \\ $$$$=\mathrm{cos}\left(\pi−\frac{\mathrm{3}\pi}{\mathrm{13}}\right)+\mathrm{cos}\left(\pi−\frac{\mathrm{5}\pi}{\mathrm{13}}\right)+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{13}}+\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{13}} \\ $$$$=\:−\mathrm{cos}\frac{\mathrm{3}\pi}{\mathrm{13}}−\mathrm{cos}\frac{\mathrm{5}\pi}{\mathrm{13}}+\mathrm{cos}\frac{\mathrm{3}\pi}{\mathrm{13}}+\mathrm{cos}\frac{\mathrm{5}\pi}{\mathrm{13}}\:=\:\mathrm{0} \\…

Solve-the-equation-x-3-mod-5-x-4-mod-7-x-2-mod-3-

Question Number 86791 by TawaTawa1 last updated on 31/Mar/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\:\:\:\:\mathrm{x}\:\:\equiv\:\:\mathrm{3}\:\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$$\:\:\:\:\mathrm{x}\:\:\equiv\:\:\mathrm{4}\:\left(\mathrm{mod}\:\mathrm{7}\right) \\ $$$$\:\:\:\:\mathrm{x}\:\:\equiv\:\:\mathrm{2}\:\left(\mathrm{mod}\:\mathrm{3}\right) \\ $$ Answered by mr W last updated on…

the-hcf-of-two-numbers-is-75-and-their-lcm-is-3375-if-one-of-the-numbers-is-675-find-the-other-number-

Question Number 21253 by gopikrishnan005@gmail.com last updated on 17/Sep/17 $${the}\:{hcf}\:{of}\:{two}\:{numbers}\:{is}\:\mathrm{75}\:{and}\:{their}\:{lcm}\:{is}\:\mathrm{3375}\:{if}\:{one}\:{of}\:{the}\:{numbers}\:{is}\:\mathrm{675}\:{find}\:{the}\:{other}\:{number} \\ $$ Answered by Tinkutara last updated on 17/Sep/17 $$\mathrm{Product}\:\mathrm{of}\:\mathrm{two}\:\mathrm{numbers}\:=\:\mathrm{HCF}×\mathrm{LCM} \\ $$$$\mathrm{675}×{x}=\mathrm{75}×\mathrm{3375} \\ $$$${x}=\mathrm{375} \\…

1-sinx-cosx-dx-

Question Number 152326 by mathdanisur last updated on 27/Aug/21 $$\int\sqrt{\frac{\mathrm{1}\:+\:\mathrm{sin}\boldsymbol{\mathrm{x}}}{\mathrm{cos}\boldsymbol{\mathrm{x}}}}\:\mathrm{dx}\:=\:? \\ $$ Commented by puissant last updated on 27/Aug/21 $$=\int\sqrt{{secx}+{tanx}}{dx} \\ $$$${Q}\mathrm{151568}\: \\ $$ Answered…

prove-x-1-x-n-y-1-y-n-R-x-1-x-2-x-n-y-1-y-2-y-n-x-1-y-1-x-2-y-2-x-n-y-n-

Question Number 21252 by youssoufab last updated on 17/Sep/17 $${prove},\forall{x}_{\mathrm{1}} ,…,{x}_{{n}} {y}_{\mathrm{1}} ,…,{y}_{{n}} \in\mathbb{R}^{+} \\ $$$$\sqrt{{x}_{\mathrm{1}} {x}_{\mathrm{2}} …{x}_{{n}} }+\sqrt{{y}_{\mathrm{1}} {y}_{\mathrm{2}} …{y}_{{n}} }\leqslant\sqrt{\left({x}_{\mathrm{1}} +{y}_{\mathrm{1}} \right)\left({x}_{\mathrm{2}} +{y}_{\mathrm{2}}…