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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

probably, cos nx=2^(n−1) cos^n x−n2^(n−3) cos^(n−2) +(((n−3)n)/2)2^(n−5) cos^(n−4) x… wow

$$\mathrm{probably},\:\mathrm{cos}\:{nx}=\mathrm{2}^{{n}−\mathrm{1}} \mathrm{cos}^{{n}} \:{x}−{n}\mathrm{2}^{{n}−\mathrm{3}} \mathrm{cos}^{{n}−\mathrm{2}} \: \\ $$$$+\frac{\left({n}−\mathrm{3}\right){n}}{\mathrm{2}}\mathrm{2}^{{n}−\mathrm{5}} \mathrm{cos}^{{n}−\mathrm{4}} \:{x}\ldots \\ $$$$\mathrm{wow} \\ $$

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 Σ_(n=1) ^∞ (((−1)^n )/(4n^2 −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 Σ_(n=2) ^∞ (((−1)^n )/(n^2 −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(x−(1/x)=7)thenthevalueofx^4 +(1/x^4 )is?

$$ \\ $$$${If}\left({x}−\frac{\mathrm{1}}{{x}}=\mathrm{7}\right){thenthevalueofx}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }{is}? \\ $$

Question Number 43224    Answers: 1   Comments: 0

how many square in a chess board.

$${how}\:{many}\:{square}\:{in}\:{a}\:{chess}\:{board}. \\ $$

Question Number 43267    Answers: 0   Comments: 2

cos 2x=2cos^2 −1 cos 3x=4cos^3 x−3cos x cos 4x=8cos^4 x−8cos^2 x+1 cos 5x=16cos^5 x−20cos^3 +5cos x cos 6x=32cos^6 x−48cos^4 x+18cos^2 x−1 cos 7x=64cos^7 x−112cos^5 x+56cos^3 x−4cos x cos 8x=128cos^8 x−256cos^6 x+160cos^4 x−32cos^2 x+1

$$\mathrm{cos}\:\mathrm{2}{x}=\mathrm{2cos}^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{3}{x}=\mathrm{4cos}^{\mathrm{3}} \:{x}−\mathrm{3cos}\:{x} \\ $$$$\mathrm{cos}\:\mathrm{4}{x}=\mathrm{8cos}^{\mathrm{4}} \:{x}−\mathrm{8cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{5}{x}=\mathrm{16cos}^{\mathrm{5}} \:{x}−\mathrm{20cos}^{\mathrm{3}} +\mathrm{5cos}\:{x}\: \\ $$$$\mathrm{cos}\:\mathrm{6}{x}=\mathrm{32cos}^{\mathrm{6}} \:{x}−\mathrm{48cos}^{\mathrm{4}} \:{x}+\mathrm{18cos}^{\mathrm{2}} \:{x}−\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{7}{x}=\mathrm{64cos}^{\mathrm{7}} \:{x}−\mathrm{112cos}^{\mathrm{5}} \:{x}+\mathrm{56cos}^{\mathrm{3}} \:{x}−\mathrm{4cos}\:{x} \\ $$$$\mathrm{cos}\:\mathrm{8}{x}=\mathrm{128cos}^{\mathrm{8}} \:{x}−\mathrm{256cos}^{\mathrm{6}} \:{x}+\mathrm{160cos}^{\mathrm{4}} \:{x}−\mathrm{32cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$

Question Number 43266    Answers: 1   Comments: 0

cos^3 x+cos^(−3) x=0 sin 2x+cos 2x=...

$$\mathrm{cos}^{\mathrm{3}} {x}+\mathrm{cos}^{−\mathrm{3}} {x}=\mathrm{0} \\ $$$$\mathrm{sin}\:\mathrm{2}{x}+\mathrm{cos}\:\mathrm{2}{x}=... \\ $$

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 ∫((lnx)/((1+x)^2 ))

$${integrate}\:{by}\:{use}\:{a}\:{partial}\:{friction} \\ $$$$\int\frac{{lnx}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} } \\ $$

Question Number 43190    Answers: 1   Comments: 1

a point move in such away that its its distance from the x−axis is alwa yas(1/5) its distance from origin. find the equetion of its path.

$${a}\:{point}\:{move}\:{in}\:{such}\:{away}\:{that}\:{its}\: \\ $$$${its}\:{distance}\:{from}\:{the}\:{x}−{axis}\:{is}\:{alwa} \\ $$$${yas}\frac{\mathrm{1}}{\mathrm{5}}\:{its}\:{distance}\:{from}\:{origin}. \\ $$$${find}\:{the}\:{equetion}\:{of}\:{its}\:{path}. \\ $$

Question Number 43180    Answers: 1   Comments: 1

The smallest and the largest values of tan^(−1) (((1−x)/(1+x))) , 0≤ x ≤ 1 are

$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{and}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)\:,\:\:\mathrm{0}\leqslant\:{x}\:\leqslant\:\mathrm{1}\:\:\mathrm{are} \\ $$

Question Number 43179    Answers: 1   Comments: 0

The solution of sin^(−1) (((2a)/(1+a^2 )))−cos^(−1) (((1−b^2 )/(1+b^2 )))=tan^(−1) (((2x)/(1−x^2 ))) is

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{a}}{\mathrm{1}+{a}^{\mathrm{2}} }\right)−\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{b}^{\mathrm{2}} }{\mathrm{1}+{b}^{\mathrm{2}} }\right)=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:\mathrm{is} \\ $$

Question Number 43187    Answers: 2   Comments: 1

Question Number 43159    Answers: 1   Comments: 0

Question Number 43158    Answers: 2   Comments: 1

∫cosecxdx

$$\int{cosecxdx} \\ $$

Question Number 43157    Answers: 1   Comments: 2

∫secxdx

$$\int{secxdx} \\ $$

Question Number 43156    Answers: 1   Comments: 0

integrate w.r.t x ∫((xe^x )/(√(1+x^2 )))dx

$${integrate}\:{w}.{r}.{t}\:{x} \\ $$$$\int\frac{{xe}^{{x}} }{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$

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