Question Number 141627 by cherokeesay last updated on 21/May/21 Answered by MJS_new last updated on 21/May/21 $$\frac{\mathrm{sin}\:\mathrm{2}{x}\:+\mathrm{sin}\:\mathrm{4}{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}\:+\mathrm{cos}\:\mathrm{4}{x}}=\frac{−\mathrm{2sin}\:{x}\:\mathrm{cos}\:{x}\:\left(\mathrm{1}−\mathrm{4cos}^{\mathrm{2}} \:{x}\right)}{\mathrm{1}+\mathrm{2cos}^{\mathrm{2}} \:{x}\:\left(\mathrm{1}−\mathrm{4sin}^{\mathrm{2}} \:{x}\right)}= \\ $$$$\:\:\:\:\:\left[\mathrm{sin}\:{x}\:=\frac{\mathrm{tan}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \:{x}}}\wedge\mathrm{cos}\:{x}\:=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \:{x}}}\right] \\…
Question Number 76088 by aliesam last updated on 23/Dec/19 Commented by mr W last updated on 23/Dec/19 $${r}=\mathrm{5} \\ $$$${see}\:{Q}#\mathrm{64112} \\ $$ Commented by aliesam…
Question Number 10553 by shiv ram last updated on 17/Feb/17 $$\left(\mathrm{D}^{\mathrm{2}} +\mathrm{4}\right)\mathrm{y}=\mathrm{tan}\:\mathrm{2x}\:\:\:\:\:\:\:\:\:\:\:\mathrm{D}=\mathrm{d}/\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76086 by hejdj last updated on 23/Dec/19 $${what}\:{is}\:{minimal}\:{expression}\:{for}\:\mathrm{sin}\:\frac{\pi}{{k}}\: \\ $$$$\mathrm{cos}\:\frac{\pi}{{k}},\:\mathrm{tan}\:\frac{\pi}{{k}},\:\mathrm{cosec}\:\frac{\pi}{{k}},\mathrm{sec}\:\frac{\pi}{{k}}{and}\:\mathrm{cot}\:\frac{\pi}{{k}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76087 by aliesam last updated on 23/Dec/19 Answered by mr W last updated on 23/Dec/19 Commented by mr W last updated on 23/Dec/19…
Question Number 141623 by qaz last updated on 21/May/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx}\right)^{\mathrm{2}} ={ln}\:\mathrm{2} \\ $$ Answered by mindispower last updated on 21/May/21…
Question Number 10547 by Saham last updated on 17/Feb/17 $$\mathrm{A}\:\mathrm{man}\:\mathrm{can}\:\mathrm{row}\:\mathrm{a}\:\mathrm{boat}\:\mathrm{at}\:\mathrm{4}\:\mathrm{km}/\mathrm{hr}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water}. \\ $$$$\mathrm{He}\:\mathrm{rows}\:\mathrm{the}\:\mathrm{boat}\:\mathrm{2km}\:\mathrm{upstream}\:\mathrm{and}\:\mathrm{2km}\:\mathrm{back}\:\mathrm{to} \\ $$$$\mathrm{his}\:\mathrm{starting}\:\mathrm{place}\:\mathrm{in}\:\mathrm{2}\:\mathrm{hours}.\:\mathrm{How}\:\mathrm{fast}\:\mathrm{is}\:\mathrm{the}\:\mathrm{stream} \\ $$$$\mathrm{flowing}\:? \\ $$ Answered by mrW1 last updated on 17/Feb/17…
Question Number 10543 by j.masanja06@gmail.com last updated on 17/Feb/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 141612 by Raxreedoroid last updated on 21/May/21 $$\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} {C}_{{k}−\mathrm{1}} ^{\:{n}−\mathrm{2}} }{\left({k}+\mathrm{1}\right)^{{x}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10542 by FilupS last updated on 17/Feb/17 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{tan}\left(\mathrm{sec}^{−\mathrm{1}} \left(\sqrt{\mathrm{tan}\left(\theta\right)}\right)\right)=\sqrt{\mathrm{tan}\left(\theta\right)}\sqrt{\mathrm{1}−\mathrm{cot}\left(\theta\right)} \\ $$ Answered by mrW1 last updated on 17/Feb/17 $${let}\:\alpha=\mathrm{sec}^{−\mathrm{1}} \left(\sqrt{\mathrm{tan}\:\left(\theta\right)}\right) \\…