Question Number 20559 by khamizan833@gmail.com last updated on 28/Aug/17 Answered by Tinkutara last updated on 28/Aug/17 $${Squaring}\:{and}\:{adding}\:{the}\:{two}\:{equations}, \\ $$$$\mathrm{9}+\mathrm{16}+\mathrm{24}\left(\mathrm{sin}\:{A}\mathrm{cos}\:{B}+\mathrm{cos}\:{A}\mathrm{sin}\:{B}\right)=\mathrm{1} \\ $$$$\mathrm{24sin}\:\left({A}+{B}\right)=−\mathrm{24} \\ $$$$\mathrm{sin}\:{C}=−\mathrm{1}\Rightarrow{This}\:{condition}\:{is}\:{not} \\ $$$${possible}.\:{Some}\:{error}\:{in}\:{the}\:{question}.…
Question Number 151630 by mathlove last updated on 22/Aug/21 Answered by qaz last updated on 22/Aug/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{H}_{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}\underset{\mathrm{n}=\mathrm{1}}…
Question Number 20558 by khamizan833@gmail.com last updated on 28/Aug/17 Commented by ajfour last updated on 28/Aug/17 $${full}\:{form}\:{of}\:\mathrm{cot}\:{x}\:{is}\:{cotangent}\:{x}. \\ $$ Answered by Tinkutara last updated on…
Question Number 151622 by otchereabdullai@gmail.com last updated on 22/Aug/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{inequality}\:\mathrm{with}\:\mathrm{integer}\: \\ $$$$\mathrm{coefficient}\:\mathrm{for}\:\mathrm{the}\:\mathrm{given}\:\mathrm{solution}\:\mathrm{set} \\ $$$$\mathrm{x}:\mathrm{x}\:<\:\frac{−\mathrm{2}}{\mathrm{5}}\:\mathrm{or}\:>\frac{\mathrm{2}}{\mathrm{5}} \\ $$ Answered by Rasheed.Sindhi last updated on 22/Aug/21 $$\mathrm{x}\:<\:\frac{−\mathrm{2}}{\mathrm{5}}\:\mathrm{or}\:>\frac{\mathrm{2}}{\mathrm{5}} \\…
Question Number 86041 by M±th+et£s last updated on 26/Mar/20 $$\left.\mathrm{1}\right){if}\: \\ $$$${sin}\left(\theta−{x}\right)={k}\:{sin}\left(\theta+\alpha\right) \\ $$$${find}\:{tan}\left(\theta\right)\:{and}\:{k} \\ $$$$ \\ $$$${then}\:{find}\:\theta\:{in}\left[\mathrm{0},\mathrm{2}\pi\right]\:\:{when}\:{k}=\frac{\mathrm{1}}{\mathrm{2}}\:{and}\:\alpha=\pi \\ $$$$ \\ $$$$\left.\mathrm{2}\right){if}\:{x}={sin}\left({t}\right)\:\:{and}\:\:{y}={cos}\left(\mathrm{2}{t}\right) \\ $$$${show}\:{that} \\…
Question Number 151568 by tabata last updated on 21/Aug/21 $$\int\:\sqrt{{sec}\left({x}\right)+{tan}\left({x}\right)}\:{dx} \\ $$$$ \\ $$$${how}\:{can}\:{it}\:{solve} \\ $$ Answered by puissant last updated on 22/Aug/21 $$=\int\sqrt{\frac{\mathrm{1}}{{cosx}}+\frac{{sinx}}{{cosx}}}{dx} \\…
Question Number 86024 by MJS last updated on 26/Mar/20 $$\mathrm{last}\:\mathrm{three}\:\mathrm{digits}\:\mathrm{of} \\ $$$$\mathrm{951413}^{\mathrm{314159}} =? \\ $$ Commented by naka3546 last updated on 26/Mar/20 $$\mathrm{277} \\ $$…
Question Number 86025 by Maclaurin Stickker last updated on 26/Mar/20 $${find}\:{the}\:{three}\:{last}\:{digits}\:{of}\:\:\mathrm{7}^{\mathrm{2020}} . \\ $$ Commented by MJS last updated on 26/Mar/20 $$\mathrm{you}\:\mathrm{can}\:\mathrm{do}\:\mathrm{it}\:\mathrm{yourself}.\:\mathrm{find}\:\mathrm{out},\:\mathrm{after}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{steps}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{repeat} \\…
Question Number 86018 by Maclaurin Stickker last updated on 26/Mar/20 $${Find}\:{the}\:{three}\:{last}\:{digits}\:{of}\:\mathrm{5}^{\mathrm{9999}} . \\ $$ Answered by MJS last updated on 26/Mar/20 $$\mathrm{5}^{\mathrm{1}} \:\:\:\:\:\mathrm{005} \\ $$$$\mathrm{5}^{\mathrm{2}}…
Question Number 85961 by A8;15: last updated on 26/Mar/20 Commented by MJS last updated on 26/Mar/20 $$\mathrm{we}\:\mathrm{still}\:\mathrm{do}\:\mathrm{not}\:\mathrm{know}\:\mathrm{what}\:{V}_{{a}} ^{{b}} \:\mathrm{is} \\ $$ Commented by jagoll last…