Question Number 134705 by bramlexs22 last updated on 06/Mar/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\:\:\:\:\:\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)\:\mathrm{cos}\:\mathrm{2x}\:+\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{1} \\ $$ Answered by john_santu last updated on 06/Mar/21 $$\:{We}\:{can}\:{setting}\:\rightarrow\begin{cases}{{X}=\mathrm{cos}\:\mathrm{2}{x}}\\{{Y}=\mathrm{sin}\:\mathrm{2}{x}}\end{cases} \\ $$$${so}\:{the}\:{equation}\:{becomes}\:\begin{cases}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right){X}+{Y}\:=\:\mathrm{1}}\\{{X}^{\mathrm{2}} +{Y}^{\:\mathrm{2}}…
Question Number 134704 by I want to learn more last updated on 06/Mar/21 Answered by mr W last updated on 07/Mar/21 Commented by mr W…
Question Number 69168 by rajesh4661kumar@gmail.com last updated on 21/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69167 by rajesh4661kumar@gmail.com last updated on 21/Sep/19 Answered by petrochengula last updated on 21/Sep/19 $${from}\:{tan}^{−\mathrm{1}} \left(\frac{{x}+{y}}{\mathrm{1}−{xy}}\right)={tan}^{−\mathrm{1}} {x}+{tan}^{−\mathrm{1}} {y} \\ $$$${tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{x}−{x}^{\mathrm{2}} }\right)={tan}^{−\mathrm{1}} \left(\frac{{x}+{x}−\mathrm{1}}{\mathrm{1}−{x}\left({x}−\mathrm{1}\right)}\right)={tan}^{−\mathrm{1}}…
Question Number 3630 by prakash jain last updated on 16/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{numbers}\:{p} \\ $$$$\mathrm{such}\:\mathrm{that}\:{n}\leqslant{p}\leqslant\mathrm{2}^{{k}} {n}\:\mathrm{is}\:\geqslant\mathrm{2}^{{k}} {n}. \\ $$$$\underset{{n}\leqslant{p}\leqslant\mathrm{2}^{{k}} {n}} {\sum}{p}\:\:\geqslant\:\mathrm{2}^{{k}} {n}\:\:\:\:\:\left({p}−{prime}\right) \\ $$ Terms of Service…
Question Number 3628 by madscientist last updated on 16/Dec/15 $${if}\:{the}\:{fibonacci}\:{sequence}\:{is}\: \\ $$$$\mathrm{1},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{8},\mathrm{13},\mathrm{21},\mathrm{34}… \\ $$$${where}\:{it}\:{is}\:\mathrm{1}+\mathrm{1}=\mathrm{2},\:\mathrm{2}+\mathrm{3}=\mathrm{5},\:\mathrm{3}+\mathrm{5}=\mathrm{8},… \\ $$$${how}\:{can}\:{we}\:{represent}\:{this}\:{sequence}\: \\ $$$${in}\:{summitation}\:{notation}\:\Sigma \\ $$$${or}\:{product}\:{notation}\:\Pi? \\ $$ Commented by 123456…
Question Number 69162 by Learner-123 last updated on 20/Sep/19 $${Find}\:{the}\:{local}\:{extreme}\:{values}\:{of} \\ $$$${the}\:{function}\:: \\ $$$${f}\left({x},{y}\right)=\:{xy}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{2}{y}+\mathrm{4}. \\ $$ Answered by MJS last updated on 20/Sep/19…
Question Number 134693 by Engr_Jidda last updated on 06/Mar/21 $$\int{sec}^{\mathrm{4}} {xtanxdx}?? \\ $$ Answered by john_santu last updated on 06/Mar/21 $$\mathcal{X}=\int\left(\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{1}\right)\mathrm{tan}\:{x}\:\mathrm{sec}\:^{\mathrm{2}} {x}\:{dx} \\ $$$${let}\:\mathrm{tan}\:{x}\:=\:\rho\:…
Question Number 69159 by Rio Michael last updated on 20/Sep/19 $${please}\:{help}\: \\ $$$$\:{A}\:\mathrm{7}.\mathrm{38}\:{g}\:{sample}\:{of}\:{magnesium}\:{sulfate}\:{MgSO}_{\mathrm{4}} .\:{X}\:{H}_{\mathrm{2}} {O}\:{lost}\:\mathrm{3}.\mathrm{78}{g}\:{of} \\ $$$${water}\:{on}\:{heating},\:{find}\:{the}\:{value}\:{of}\:{X}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 134694 by Engr_Jidda last updated on 06/Mar/21 $$\int{sin}^{\mathrm{4}} {xdx} \\ $$ Answered by john_santu last updated on 06/Mar/21 $$\mathcal{J}\:=\:\int\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2}{x}\right)^{\mathrm{2}} {dx} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{4}}\int\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}\right)^{\mathrm{2}} \:{dx}…