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Author: Tinku Tara

sin-1-2-5-find-cos-and-tan-

Question Number 126700 by Eric002 last updated on 23/Dec/20 $$\theta={sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{5}}\right)\:{find}\:{cos}\left(\theta\right)\:{and}\:{tan}\left(\theta\right) \\ $$$$ \\ $$ Answered by akornes last updated on 23/Dec/20 $${cos}\theta=\pm\frac{\sqrt{\mathrm{21}}}{\mathrm{5}}\:{and}\:{tan}\theta=\pm\frac{\mathrm{2}\sqrt{\mathrm{21}}}{\mathrm{21}} \\ $$…

Question-61165

Question Number 61165 by Tawa1 last updated on 29/May/19 Answered by MJS last updated on 30/May/19 $$\int\frac{\mathrm{cos}^{\mathrm{2}} \:\left(\mathrm{2}{x}−\mathrm{5}\right)\:\mathrm{cos}\:\left(\mathrm{2}{x}−\mathrm{14}\right)}{\mathrm{cos}\:\left(\mathrm{2}{x}−\mathrm{7}\right)}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{2}{x}−\mathrm{7}\:\rightarrow\:{dx}=\frac{{dt}}{\mathrm{2}}\right] \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{cos}^{\mathrm{2}} \:\left({t}+\mathrm{2}\right)\:\mathrm{cos}\:\left({t}−\mathrm{7}\right)}{\mathrm{cos}\:\left({t}\right)}{dt}= \\ $$$$\:\:\:\:\:\left[\mathrm{use}\:\mathrm{these}:\right.…

show-for-all-n-N-that-3-1-5-n-5-is-divisible-by-1-3-n-3-

Question Number 192233 by gatocomcirrose last updated on 12/May/23 $$\mathrm{show}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\in\mathrm{N}\:\mathrm{that} \\ $$$$\mathrm{3}\left(\mathrm{1}^{\mathrm{5}} +…+\mathrm{n}^{\mathrm{5}} \right)\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{1}^{\mathrm{3}} +…+\mathrm{n}^{\mathrm{3}} \\ $$ Commented by Frix last updated on 12/May/23 $${S}_{\mathrm{5}}…

if-sin-x-x-20-20-find-x-

Question Number 61162 by Tawa1 last updated on 29/May/19 $$\mathrm{if}\:\:\:\:\:\mathrm{sin}\left(\mathrm{x}\right)\:\:=\:\:\frac{\mathrm{x}\:−\:\mathrm{20}}{\mathrm{20}}\:\:,\:\:\:\mathrm{find}\:\:\mathrm{x} \\ $$ Commented by kaivan.ahmadi last updated on 29/May/19 $${we}\:{can}\:{find}\:{number}\:{of}\:{solution}\:{by}\:{plote} \\ $$$${y}={sinx}\:{and}\:{y}=\frac{{x}−\mathrm{20}}{\mathrm{20}} \\ $$$${this}\:{equation}\:{has}\:\mathrm{13}\:{answer} \\…