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Category: Algebra

Show-that-1-1-sinz-1-z-n-1-1-n-1-z-npi-1-z-npi-2-cotz-1-z-n-1-1-z-npi-1-z-npi-where-z-mpi-m-Z-given-the-fact-that-cosax-2sinapi-pi-1-2a-n-1-

Question Number 1838 by 112358 last updated on 11/Oct/15 $${Show}\:{that} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{1}}{{sinz}}=\frac{\mathrm{1}}{{z}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left(\frac{\mathrm{1}}{{z}+{n}\pi}+\frac{\mathrm{1}}{{z}−{n}\pi}\right) \\ $$$$\left(\mathrm{2}\right)\:{cotz}=\frac{\mathrm{1}}{{z}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{z}+{n}\pi}+\frac{\mathrm{1}}{{z}−{n}\pi}\right) \\ $$$${where}\:{z}\neq{m}\pi,\:{m}\in\mathbb{Z}\:,\:{given}\:{the}\:{fact}\:{that} \\ $$$${cosax}=\frac{\mathrm{2}{sina}\pi}{\pi}\left[\frac{\mathrm{1}}{\mathrm{2}{a}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}}…

Question-67371

Question Number 67371 by TawaTawa last updated on 26/Aug/19 Answered by mind is power last updated on 26/Aug/19 $${a}^{\mathrm{2}} \mathrm{3}{b}={b}^{\mathrm{3}} +\mathrm{9}\sqrt{\mathrm{3}}…\mathrm{1} \\ $$$${b}^{\mathrm{2}} \mathrm{3}{a}={a}^{\mathrm{3}} −\mathrm{10}….\mathrm{2}…

a-pinhole-camera-is-placed-300cm-in-front-of-a-building-so-that-the-image-is-formed-on-a-screen-5cm-from-the-pin-hole-if-the-image-is-2-5cm-high-the-height-of-the-building-will-be-

Question Number 132900 by aurpeyz last updated on 17/Feb/21 $${a}\:{pinhole}\:{camera}\:{is}\:{placed}\:\mathrm{300}{cm} \\ $$$${in}\:{front}\:{of}\:{a}\:{building}\:{so}\:{that}\:{the}\:{image} \\ $$$${is}\:{formed}\:{on}\:{a}\:{screen}\:\mathrm{5}{cm}\:{from}\:{the} \\ $$$${pin}\:{hole}.\:{if}\:{the}\:{image}\:{is}\:\mathrm{2}.\mathrm{5}{cm}\:{high}. \\ $$$${the}\:{height}\:{of}\:{the}\:{building}\:{will}\:{be}? \\ $$ Commented by mr W last…

m-p-1-a-q-p-1-r-1-b-amp-p-p-1-q-1-c-and-r-p-1-m-1-d-find-either-of-p-q-r-m-in-terms-of-a-b-c-d-

Question Number 67337 by ajfour last updated on 25/Aug/19 $${m}\left({p}+\mathrm{1}\right)={a} \\ $$$$\frac{{q}\left({p}+\mathrm{1}\right)}{{r}+\mathrm{1}}={b}\:\:\&\:\:\frac{{p}\left({p}+\mathrm{1}\right)}{{q}+\mathrm{1}}={c} \\ $$$${and}\:\:\frac{{r}\left({p}+\mathrm{1}\right)}{{m}+\mathrm{1}}={d} \\ $$$${find}\:{either}\:{of}\:{p},{q},{r},{m}\:{in}\:{terms}\:{of} \\ $$$${a},{b},{c},{d}. \\ $$ Answered by mr W last…

Let-f-be-a-function-defined-on-the-domain-D-f-C-and-f-z-cosz-for-z-D-f-Is-f-z-a-member-of-C-Compute-for-example-f-2-6i-

Question Number 1797 by 112358 last updated on 29/Sep/15 $${Let}\:{f}\:{be}\:{a}\:{function}\:{defined}\:{on} \\ $$$${the}\:{domain}\:{D}_{{f}} =\mathbb{C}\:{and}\:{f}\left({z}\right)={cosz} \\ $$$${for}\:{z}\in{D}_{{f}} \:.\:{Is}\:{f}\left({z}\right)\:{a}\:{member} \\ $$$${of}\:\mathbb{C}?\:{Compute}\:{for}\:{example} \\ $$$${f}\left(\mathrm{2}+\mathrm{6}{i}\right). \\ $$$$ \\ $$ Answered…

Simplify-log-3-4i-7-24i-

Question Number 1794 by Rasheed Soomro last updated on 29/Sep/15 $${Simplify} \\ $$$${log}_{\left(\mathrm{3}+\mathrm{4}{i}\right)} \left(−\mathrm{7}+\mathrm{24}{i}\right) \\ $$ Commented by 112358 last updated on 29/Sep/15 $${Define}\:{p}={log}_{\left(\mathrm{3}+\mathrm{4}{i}\right)} \left(−\mathrm{7}+\mathrm{24}{i}\right)…