Question Number 20102 by ajfour last updated on 21/Aug/17 $${Solve}\:{the}\:{equation}: \\ $$$$\left(\mathrm{log}\:_{\mathrm{sin}\:{x}} \mathrm{cos}\:{x}\right)^{\mathrm{2}} =\mathrm{1} \\ $$ Answered by allizzwell23 last updated on 21/Aug/17 $$\:\:\mathrm{log}_{\mathrm{sin}\:{x}} \mathrm{cos}\:{x}\:=\:\mathrm{1}…
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Question Number 151174 by mathdanisur last updated on 18/Aug/21 $$\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot…}}}}}}\:\:=\:\mathrm{3}\: \\ $$$$\mathrm{find}\:\:{a}=? \\ $$ Answered by mr W last updated on 18/Aug/21 $$\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}×\mathrm{3}}}=\mathrm{3} \\ $$$${a}+\mathrm{3}=\mathrm{27}…
Question Number 85637 by jagoll last updated on 23/Mar/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\: \\ $$ Commented by abdomathmax last updated on 23/Mar/20 $${I}\:=\int\:\:\frac{{dx}}{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:\:{we}\:{do}\:{the}\:{changement}\:{x}={sh}\left({t}\right)\:\Rightarrow \\ $$$${I}\:=\int\:\:\frac{{cht}}{{sht}\:+{cht}}{dt}\:=\int\:\:\frac{{e}^{{t}} \:+{e}^{−{t}}…
Question Number 85630 by Roland Mbunwe last updated on 23/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{2}\Pi} \:\:\:\frac{{dx}}{\:\sqrt{\mathrm{2}}−{cosx}}\:\: \\ $$ Commented by MJS last updated on 23/Mar/20 $$\mathrm{see}\:\mathrm{question}\:\mathrm{85568} \\ $$…
Question Number 151164 by puissant last updated on 18/Aug/21 Commented by puissant last updated on 18/Aug/21 $${solve}\:{in}\:\mathbb{R} \\ $$ Answered by MJS_new last updated on…
Question Number 20091 by Tinkutara last updated on 21/Aug/17 $$\mathrm{Prove}\:\mathrm{that}\:\underset{{n}=\mathrm{0}} {\overset{\mathrm{3}} {\sum}}\mathrm{tan}^{\mathrm{2}} \:\frac{\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\pi}{\mathrm{16}}\:=\:\mathrm{28}. \\ $$ Answered by ajfour last updated on 21/Aug/17 $$\frac{\mathrm{sin}\:^{\mathrm{2}} {A}}{\mathrm{cos}\:^{\mathrm{2}} {A}}+\frac{\mathrm{sin}\:^{\mathrm{2}}…
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Question Number 151162 by tabata last updated on 18/Aug/21 Commented by tabata last updated on 18/Aug/21 $${how}\:{can}\:{it}\:{solve} \\ $$ Commented by mr W last updated…
Question Number 85625 by jagoll last updated on 23/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{n}} −\left(\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{n}} }{\left(\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{n}+\mathrm{2}} } \\ $$ Answered by john santu last updated on 23/Mar/20 $${by}\:{Maclaurin}\:{series}…