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Question Number 166169 Answers: 1 Comments: 0

sin^7 (x)+(1/(sin^3 (x)))=cos^7 (x)+(1/(cos^3 (x)))

$$\:\:\mathrm{sin}^{\mathrm{7}} \left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)}=\mathrm{cos}\:^{\mathrm{7}} \left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{x}\right)} \\ $$$$ \\ $$

Question Number 166168 Answers: 0 Comments: 0

prove Σ_(r=−∞) ^∞ (1/(x + (r+(1/2))π)) = tan(x) (Σ_(r=−∞) ^∞ (1/(x + r)))(Σ_(r=−∞) ^∞ (1/(x + r))) = −(π^2 /4) ( r = odd) (r = even)

$${prove} \\ $$$$\underset{{r}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{x}\:+\:\left({r}+\frac{\mathrm{1}}{\mathrm{2}}\right)\pi}\:=\:{tan}\left({x}\right) \\ $$$$\left(\underset{{r}=−\infty} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{x}\:+\:{r}}\right)\left(\underset{{r}=−\infty} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{x}\:+\:{r}}\right)\:=\:−\frac{\pi^{\mathrm{2}} }{\mathrm{4}} \\ $$$$\:\:\:\:\:\left(\:{r}\:=\:{odd}\right)\:\:\:\:\:\:\:\:\left({r}\:=\:{even}\right) \\ $$

Question Number 166167 Answers: 0 Comments: 0

Question Number 166163 Answers: 0 Comments: 0

Question Number 166215 Answers: 1 Comments: 0

Question Number 166260 Answers: 1 Comments: 0

∫_0 ^(π/2) ln(sinx+cosx)dx=? −−−−−−−−−−−−by M.A

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{cosx}}\right)\boldsymbol{\mathrm{dx}}=? \\ $$$$−−−−−−−−−−−−\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{M}}.\boldsymbol{\mathrm{A}} \\ $$

Question Number 166160 Answers: 3 Comments: 0

Σ_(n=1) ^∞ Σ_(m=1) ^∞ (1/(m^2 n+mn^2 +2mn))=?

$$\:\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{m}^{\mathrm{2}} \mathrm{n}+\mathrm{mn}^{\mathrm{2}} +\mathrm{2mn}}=? \\ $$

Question Number 166143 Answers: 1 Comments: 0

Question Number 166141 Answers: 2 Comments: 0

∫_0 ^x (t^2 /( (√(a+2t^2 ))))dt

$$\int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \frac{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }{\:\sqrt{\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{t}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dt}}\: \\ $$

Question Number 166137 Answers: 2 Comments: 0

Question Number 166135 Answers: 1 Comments: 1

find the domain of f(x) = (1/([x]−1))

$${find}\:{the}\:{domain}\:{of}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left[{x}\right]−\mathrm{1}} \\ $$

Question Number 166134 Answers: 1 Comments: 0

Question Number 166127 Answers: 0 Comments: 0

Question Number 166125 Answers: 0 Comments: 0

Question Number 166120 Answers: 1 Comments: 2

Question Number 166113 Answers: 2 Comments: 2

prove that 1!=1

$${prove}\:{that}\:\mathrm{1}!=\mathrm{1} \\ $$

Question Number 166112 Answers: 1 Comments: 1

prove that 0!=1

$${prove}\:{that}\:\mathrm{0}!=\mathrm{1} \\ $$

Question Number 166111 Answers: 1 Comments: 0

Question Number 166110 Answers: 1 Comments: 0

Prove that ((( n)),(( 0)) )^2 + ((( n)),(( 1)) )^2 + ((( n)),(( 2)) )^2 + …+ ((( n)),(( n)) )^2 = ((( 2n)),(( n)) )

$$\mathrm{Prove}\:\:\mathrm{that} \\ $$$$\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{0}}\end{pmatrix}^{\mathrm{2}} \:+\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{1}}\end{pmatrix}^{\mathrm{2}} \:+\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{2}}\end{pmatrix}^{\mathrm{2}} \:+\:\ldots+\:\begin{pmatrix}{\:{n}}\\{\:{n}}\end{pmatrix}^{\mathrm{2}} \:\:=\:\:\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix} \\ $$

Question Number 166104 Answers: 1 Comments: 0

Question Number 166102 Answers: 1 Comments: 0

Question Number 166241 Answers: 2 Comments: 0

x^5 −1=0 please how do i find for all the values of x?

$$\:\boldsymbol{{x}}^{\mathrm{5}} −\mathrm{1}=\mathrm{0} \\ $$$$\:\boldsymbol{{please}}\:\boldsymbol{{how}}\:\boldsymbol{{do}}\:\boldsymbol{{i}}\:\boldsymbol{{find}}\:\boldsymbol{{for}}\:\boldsymbol{{all}}\:\boldsymbol{{the}} \\ $$$$\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}? \\ $$

Question Number 166093 Answers: 2 Comments: 3

Question Number 166089 Answers: 0 Comments: 3

Question Number 166088 Answers: 0 Comments: 0

Question Number 166087 Answers: 1 Comments: 1

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