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Question Number 43331 Answers: 0 Comments: 5
Question Number 43319 Answers: 1 Comments: 0
Question Number 43288 Answers: 0 Comments: 2
Question Number 43268 Answers: 0 Comments: 5
$$\mathrm{probably},\:\mathrm{cos}\:{nx}=\mathrm{2}^{{n}−\mathrm{1}} \mathrm{cos}^{{n}} \:{x}−{n}\mathrm{2}^{{n}−\mathrm{3}} \mathrm{cos}^{{n}−\mathrm{2}} \: \\ $$$$+\frac{\left({n}−\mathrm{3}\right){n}}{\mathrm{2}}\mathrm{2}^{{n}−\mathrm{5}} \mathrm{cos}^{{n}−\mathrm{4}} \:{x}\ldots \\ $$$$\mathrm{wow} \\ $$
Question Number 43265 Answers: 0 Comments: 3
Question Number 43264 Answers: 2 Comments: 1
Question Number 43263 Answers: 2 Comments: 0
Question Number 43260 Answers: 0 Comments: 1
$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} \:−\mathrm{1}}\:. \\ $$
Question Number 43259 Answers: 0 Comments: 1
$${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} −\mathrm{1}} \\ $$
Question Number 43252 Answers: 3 Comments: 2
Question Number 43226 Answers: 1 Comments: 0
$$ \\ $$$${If}\left({x}−\frac{\mathrm{1}}{{x}}=\mathrm{7}\right){thenthevalueofx}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }{is}? \\ $$
Question Number 43224 Answers: 1 Comments: 0
$${how}\:{many}\:{square}\:{in}\:{a}\:{chess}\:{board}. \\ $$
Question Number 43267 Answers: 0 Comments: 2
$$\mathrm{cos}\:\mathrm{2}{x}=\mathrm{2cos}^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{3}{x}=\mathrm{4cos}^{\mathrm{3}} \:{x}−\mathrm{3cos}\:{x} \\ $$$$\mathrm{cos}\:\mathrm{4}{x}=\mathrm{8cos}^{\mathrm{4}} \:{x}−\mathrm{8cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{5}{x}=\mathrm{16cos}^{\mathrm{5}} \:{x}−\mathrm{20cos}^{\mathrm{3}} +\mathrm{5cos}\:{x}\: \\ $$$$\mathrm{cos}\:\mathrm{6}{x}=\mathrm{32cos}^{\mathrm{6}} \:{x}−\mathrm{48cos}^{\mathrm{4}} \:{x}+\mathrm{18cos}^{\mathrm{2}} \:{x}−\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{7}{x}=\mathrm{64cos}^{\mathrm{7}} \:{x}−\mathrm{112cos}^{\mathrm{5}} \:{x}+\mathrm{56cos}^{\mathrm{3}} \:{x}−\mathrm{4cos}\:{x} \\ $$$$\mathrm{cos}\:\mathrm{8}{x}=\mathrm{128cos}^{\mathrm{8}} \:{x}−\mathrm{256cos}^{\mathrm{6}} \:{x}+\mathrm{160cos}^{\mathrm{4}} \:{x}−\mathrm{32cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$
Question Number 43266 Answers: 1 Comments: 0
$$\mathrm{cos}^{\mathrm{3}} {x}+\mathrm{cos}^{−\mathrm{3}} {x}=\mathrm{0} \\ $$$$\mathrm{sin}\:\mathrm{2}{x}+\mathrm{cos}\:\mathrm{2}{x}=... \\ $$
Question Number 43205 Answers: 1 Comments: 0
Question Number 43196 Answers: 0 Comments: 4
Question Number 43192 Answers: 1 Comments: 6
Question Number 43191 Answers: 1 Comments: 3
$${integrate}\:{by}\:{use}\:{a}\:{partial}\:{friction} \\ $$$$\int\frac{{lnx}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} } \\ $$
Question Number 43190 Answers: 1 Comments: 1
$${a}\:{point}\:{move}\:{in}\:{such}\:{away}\:{that}\:{its}\: \\ $$$${its}\:{distance}\:{from}\:{the}\:{x}−{axis}\:{is}\:{alwa} \\ $$$${yas}\frac{\mathrm{1}}{\mathrm{5}}\:{its}\:{distance}\:{from}\:{origin}. \\ $$$${find}\:{the}\:{equetion}\:{of}\:{its}\:{path}. \\ $$
Question Number 43180 Answers: 1 Comments: 1
$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{and}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)\:,\:\:\mathrm{0}\leqslant\:{x}\:\leqslant\:\mathrm{1}\:\:\mathrm{are} \\ $$
Question Number 43179 Answers: 1 Comments: 0
$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{a}}{\mathrm{1}+{a}^{\mathrm{2}} }\right)−\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{b}^{\mathrm{2}} }{\mathrm{1}+{b}^{\mathrm{2}} }\right)=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:\mathrm{is} \\ $$
Question Number 43187 Answers: 2 Comments: 1
Question Number 43159 Answers: 1 Comments: 0
Question Number 43158 Answers: 2 Comments: 1
$$\int{cosecxdx} \\ $$
Question Number 43157 Answers: 1 Comments: 2
$$\int{secxdx} \\ $$
Question Number 43156 Answers: 1 Comments: 0
$${integrate}\:{w}.{r}.{t}\:{x} \\ $$$$\int\frac{{xe}^{{x}} }{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$
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