Question Number 12926 by kashyappushpendrak1811@gmail.c last updated on 07/May/17 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\mathrm{log}\:\mid\mathrm{tan}\:{x}+\mathrm{cot}\:{x}\mid\:{dx}\:= \\ $$ Answered by ajfour last updated on 07/May/17 $$\mathrm{0}\leqslant{x}\leqslant\pi/\mathrm{2}\:\:\Rightarrow\:\:\:\:\:\:\mathrm{0}\leqslant\mathrm{2}{x}\leqslant\pi \\ $$$$\mathrm{tan}\:{x}+\mathrm{cot}\:{x}=\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}} \\…
Question Number 12919 by kashyappushpendrak1811@gmail.c last updated on 07/May/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{e}^{{x}^{\mathrm{2}} } {dx}\:\:\mathrm{lies} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12841 by CheaV last updated on 04/May/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}+\mathrm{5}\:\sqrt{\mathrm{2}}\:{x}\right)^{\mathrm{9}} \:+\:\left(\mathrm{1}−\mathrm{5}\:\sqrt{\mathrm{2}}\:{x}\right)^{\mathrm{9}} \:\mathrm{is} \\ $$ Answered by malwaan last updated on 04/May/17 $$\mathrm{5}\:\mathrm{terms} \\…
Question Number 12828 by 786786AM last updated on 03/May/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{infinite}\:\mathrm{product} \\ $$$$\sqrt{\mathrm{3}}\:\centerdot\:\sqrt[{\mathrm{4}}]{\mathrm{9}}\:\centerdot\:\sqrt[{\mathrm{8}}]{\mathrm{27}}\:\centerdot\:\sqrt[{\mathrm{16}}]{\mathrm{81}}\:…\mathrm{to}\:\infty\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_\_. \\ $$ Answered by prakash jain last updated on 04/May/17 $$\mathrm{3}^{\mathrm{1}/\mathrm{2}} \centerdot\mathrm{3}^{\mathrm{2}/\mathrm{4}} \centerdot\mathrm{3}^{\mathrm{3}/\mathrm{8}}…
Question Number 12827 by 786786AM last updated on 03/May/17 $$\mathrm{Sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{be}\:\mathrm{14}.\:\mathrm{If}\:\mathrm{one}\:\mathrm{is} \\ $$$$\mathrm{added}\:\mathrm{to}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{and}\:\mathrm{1}\:\mathrm{is}\:\mathrm{subtracted} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{third},\:\mathrm{the}\:\mathrm{new}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}. \\ $$$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{of}\:\mathrm{them}\:\mathrm{is} \\ $$ Answered by mrW1 last updated on 04/May/17…
Question Number 12470 by biah last updated on 23/Apr/17 $$\sqrt[{\mathrm{5}}]{\mathrm{0}.\mathrm{03125}}\:=\: \\ $$ Answered by sma3l2996 last updated on 23/Apr/17 $$=\sqrt[{\mathrm{5}}]{\frac{\mathrm{3125}}{\mathrm{10}^{\mathrm{5}} }}=\frac{\sqrt[{\mathrm{5}}]{\mathrm{5}^{\mathrm{5}} }}{\mathrm{10}}=\mathrm{0}.\mathrm{5} \\ $$ Terms…
Question Number 12170 by indreshpatelindresh@435gmail.i last updated on 15/Apr/17 $$\mathrm{In}\:\mathrm{any}\:\bigtriangleup{ABC}, \\ $$$$\:\mathrm{2}\left({bc}\:\mathrm{cos}\:{A}+{ca}\:\mathrm{cos}\:{B}+{ab}\:\mathrm{cos}\:{C}\right)\:= \\ $$ Answered by mrW1 last updated on 15/Apr/17 $${a}^{\mathrm{2}} ={b}^{\mathrm{2}} +{c}^{\mathrm{2}} −\mathrm{2}{bc}\mathrm{cos}\:{A}…
Question Number 12169 by indreshpatelindresh@435gmail.i last updated on 15/Apr/17 $$\mathrm{If}\:\:\mathrm{tan}\:\alpha\:\mathrm{equals}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{inequality}\:\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{15}<\mathrm{0}\:\mathrm{and}\: \\ $$$$\mathrm{cos}\:\beta\:\:\mathrm{equals}\:\mathrm{to}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bisector} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{quadrant},\:\mathrm{then}\: \\ $$$$\mathrm{sin}\:\left(\alpha+\beta\right)\:\mathrm{sin}\:\left(\alpha−\beta\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by mrW1 last…
Question Number 12160 by indreshpatelindresh@435gmail.i last updated on 15/Apr/17 $$\mathrm{Two}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{cot}^{−\mathrm{1}} \mathrm{2} \\ $$$$\mathrm{and}\:\mathrm{cot}^{−\mathrm{1}} \mathrm{3}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{third}\:\mathrm{angle}\:\mathrm{is} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 15/Apr/17 $${tg}\left({cot}^{−\mathrm{1}} \mathrm{2}+{cot}^{−\mathrm{1}}…
Question Number 11979 by 786786AM last updated on 08/Apr/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:{p}\:\mathrm{terms},\:\mathrm{first}\:\:{q}\:\mathrm{terms}\:\mathrm{and} \\ $$$$\mathrm{first}\:{r}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{be}\:\:{x},\:{y}\:\:\mathrm{and}\:{z}\: \\ $$$$\mathrm{respectively}.\:\mathrm{Then} \\ $$$$\frac{{x}}{{p}}\left({q}−{r}\right)\:+\:\frac{{y}}{{q}}\left({r}−{p}\right)\:+\:\frac{{z}}{{r}}\left({p}−{q}\right)\:\:\mathrm{is} \\ $$ Answered by ajfour last updated on 09/Apr/17…