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Category: Trigonometry

If-sin-23pi-24-2-p-q-1-4-r-then-the-value-of-p-2-q-2-r-2-is-equal-to-

Question Number 133142 by bemath last updated on 19/Feb/21 $$\mathrm{If}\:\mathrm{sin}\:\left(\frac{\mathrm{23}\pi}{\mathrm{24}}\right)\:=\:\sqrt{\frac{\mathrm{2}\sqrt{\mathrm{p}}−\sqrt{\mathrm{q}}−\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{r}}}} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} \right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\: \\ $$ Answered by Ñï= last updated on…

Question-67495

Question Number 67495 by TawaTawa last updated on 28/Aug/19 Commented by Prithwish sen last updated on 28/Aug/19 $$\mathrm{sin}\left(\frac{\mathrm{5}}{\mathrm{2}}\pi+\mathrm{x}\right)=\mathrm{Cos}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{9}}\right)\Rightarrow\mathrm{Cosx}=\mathrm{Cos}\left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{18}}\right) \\ $$$$\mathrm{x}=\mathrm{2n}\pi\pm\left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{18}}\right)\:\:\:\mathrm{n}\in\:\mathbb{Z} \\ $$ Commented by TawaTawa…

prove-Cos-2pi-7-Cos-4pi-7-Cos-8pi-7-1-2-

Question Number 67464 by lalitchand last updated on 27/Aug/19 $$\mathrm{prove}\:\:\:\mathrm{Cos}\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{Cos}\left(\frac{\mathrm{4}\pi}{\mathrm{7}}\right)+\mathrm{Cos}\left(\frac{\mathrm{8}\pi}{\mathrm{7}}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mind is power last updated on 27/Aug/19 $${Z}^{\mathrm{7}} −\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\left({z}−\mathrm{1}\right)\left(\mathrm{1}+{z}+{z}^{\mathrm{2}}…

Solve-for-x-tan-x-tan-2x-tan-3x-0-Some-one-had-posted-this-question-and-I-had-answered-it-but-then-thread-was-deleted-I-think-that-the-question-is-not-importanceless-so-I-hav-reposted-it-

Question Number 1890 by Rasheed Soomro last updated on 21/Oct/15 $${Solve}\:{for}\:{x} \\ $$$$\:\:\:\:\:\:{tan}\:{x}\:+{tan}\:\mathrm{2}{x}\:−{tan}\:\mathrm{3}{x}\:=\mathrm{0} \\ $$$${Some}\:{one}\:{had}\:{posted}\:{this}\:{question}\:{and}\:{I}\:{had}\:{answered}\:{it} \\ $$$${but}\:{then}\:{thread}\:{was}\:{deleted}! \\ $$$${I}\:{think}\:{that}\:{the}\:{question}\:{is}\:{not}\:{importanceless}\:,\:{so}\:{I}\:{hav} \\ $$$${reposted}\:{it}. \\ $$ Commented by…

Question-67396

Question Number 67396 by Cmr 237 last updated on 26/Aug/19 Commented by mathmax by abdo last updated on 26/Aug/19 $${let}\:{P}\left({z}\right)\:=\:{z}^{\mathrm{2}{n}} \:+\mathrm{1}\:{let}\:{determine}\:{the}\:{roots}\:{of}\:{P}\left({z}\right) \\ $$$${P}\left({z}\right)=\mathrm{0}\:\Leftrightarrow\:{z}^{\mathrm{2}{n}} \:=−\mathrm{1}\:\:\Leftrightarrow\:\:{z}^{\mathrm{2}{n}} ={e}^{{i}\left(\mathrm{2}{k}+\mathrm{1}\right)\pi}…

Show-that-given-4cos-pi-3-2-3-sin-pi-3-5-then-pi-3cos-1-5-28-3tan-1-3-2-

Question Number 1830 by 112358 last updated on 10/Oct/15 $${Show}\:{that}\:{given} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}{cos}\frac{\pi}{\mathrm{3}}+\mathrm{2}\sqrt{\mathrm{3}}{sin}\frac{\pi}{\mathrm{3}}=\mathrm{5} \\ $$$${then} \\ $$$$\:\:\:\:\:\:\:\pi=\mathrm{3}{cos}^{−\mathrm{1}} \left(\frac{\mathrm{5}}{\:\sqrt{\mathrm{28}}}\right)+\mathrm{3}{tan}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\:. \\ $$ Answered by Rasheed Soomro last…