Question Number 134328 by BHOOPENDRA last updated on 02/Mar/21 $${express}\:{f}\left({x}\right)={x}\:{as}\:{a}\:{sine}\:{series}\: \\ $$$${in}\:\mathrm{0}<{x}<\pi? \\ $$ Answered by Dwaipayan Shikari last updated on 02/Mar/21 $${log}\left(\mathrm{1}+{e}^{{ix}} \right)={log}\left(\sqrt{\mathrm{2}+\mathrm{2}{sinx}}\right)+{itan}^{−\mathrm{1}} \frac{{sinx}}{{cosx}+\mathrm{1}}…
Question Number 134331 by Mikael_786 last updated on 02/Mar/21 $$\mathrm{cos}^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{2}}−\mathrm{x}\right)=\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}+\pi\right) \\ $$$$\mathrm{0}\leqslant\mathrm{x}\leqslant\pi \\ $$$$\mathrm{x}=? \\ $$ Answered by EDWIN88 last updated on 02/Mar/21…
Question Number 134327 by mr W last updated on 02/Mar/21 Answered by aleks041103 last updated on 25/Dec/21 $${i}\Rightarrow\mid{z}_{{k}} ^{\mathrm{2}} \mid=\mathrm{1} \\ $$$$\Rightarrow{z}_{{k}} ={e}^{{it}_{{k}} } \\…
Question Number 68788 by mhmd last updated on 15/Sep/19 $$\int\mathrm{1}/\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} \:{dx} \\ $$ Commented by Prithwish sen last updated on 15/Sep/19 $$\mathrm{Using}\:\mathrm{by}\:\mathrm{parts} \\ $$$$\mathrm{I}_{\mathrm{n}}…
Question Number 134320 by mohammad17 last updated on 02/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 3250 by Filup last updated on 08/Dec/15 $$\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}: \\ $$$$\zeta\left({s}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{i}^{−{s}} \\ $$$$ \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\zeta\left({s}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{1}}{\pi\left({i}\right)^{{s}} }\right) \\ $$$$\mathrm{where}\:\pi\left({n}\right)={n}\mathrm{th}\:\mathrm{prime}…
Question Number 134323 by aurpeyz last updated on 02/Mar/21 $${A}\:{lens}\:{is}\:{required}\:{to}\:{have}\:{a}\:{power}\:{of} \\ $$$$−\mathrm{2}.\mathrm{5}\:{dioptres}\:{in}\:{air}.\:{the}\:{convex} \\ $$$${front}\:{surface}\:{has}\:{a}\:{radius}\:{of}\:{curvature} \\ $$$${of}\:\mathrm{30}{cm}.\:{calculate}\:{the}\:{radius}\:{of}\:{curvature} \\ $$$${of}\:{the}\:{rear}\:{surface} \\ $$ Answered by ajfour last updated…
Question Number 3249 by Rasheed Soomro last updated on 08/Dec/15 $$\mathcal{H}{ow}\:{could}\:\sqrt{\mathrm{5}}\:\:{be}\:{drawn}\:{on}\:{numbered}\:{line}\:{using} \\ $$$${scale}\:{and}\:{compass}\:{only}?\:\left({Exactly}\:\sqrt{\mathrm{5}}\:{not}\:{its}\:{decimal}\:{approximation}.\right) \\ $$ Answered by prakash jain last updated on 08/Dec/15 $$\mathrm{For}\:\sqrt{\mathrm{5}} \\…
Question Number 68782 by Maclaurin Stickker last updated on 06/Oct/19 $$\mathrm{Let}\:{d}_{{n}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{determinant}\:\mathrm{of}\:\mathrm{the}\:{n}×{n} \\ $$$$\mathrm{matrix}\:\mathrm{whose}\:\mathrm{entries},\:\mathrm{from}\:\mathrm{left}\:\mathrm{to}\:\mathrm{right} \\ $$$$\mathrm{and}\:\mathrm{then}\:\mathrm{from}\:\mathrm{top}\:\mathrm{to}\:\mathrm{bottom},\:\mathrm{are} \\ $$$${cos}\:\mathrm{1},\:{cos}\:\mathrm{2},\:…,\:{cos}\:{n}^{\mathrm{2}} .\:\left(\mathrm{For}\:\mathrm{example},\right. \\ $$$${d}_{\mathrm{3}} =\begin{vmatrix}{{cos}\:\mathrm{1}\:\:{cos}\:\mathrm{2}\:\:{cos}\:\mathrm{3}}\\{{cos}\:\mathrm{4}\:\:{cos}\:\mathrm{5}\:\:{cos}\:\mathrm{6}}\\{{cos}\:\mathrm{7}\:\:{cos}\:\mathrm{8}\:\:{cos}\:\mathrm{9}}\end{vmatrix}. \\ $$$$\mathrm{The}\:\mathrm{argument}\:\mathrm{of}\:{cos}\:\mathrm{is}\:\mathrm{always}\:\mathrm{in}\:\mathrm{radians} \\…
Question Number 68783 by peter frank last updated on 15/Sep/19 Commented by peter frank last updated on 22/Sep/19 $${thank}\:{you}\: \\ $$ Commented by ajfour last…