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Category: Trigonometry

elemeary-calculus-if-sin-3x-cos-3x-m-sin-x-cos-x-n-then-find-the-relatiomship-between-m-and-n-independent-of-x-

Question Number 127373 by mnjuly1970 last updated on 29/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{elemeary}\:\:\:{calculus}.. \\ $$$$\:\:{if}\:\:\:\:\begin{cases}{{sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)={m}}\\{{sin}\left({x}\right)+{cos}\left({x}\right)={n}}\end{cases} \\ $$$$\:\:\:{then}\:\:\:{find}\:{the}\:{relatiomship} \\ $$$$\:\:\:{between}\:\:'{m}'\:{and}\:'\:{n}'\:{independent}\:{of} \\ $$$$\:\:'\:{x}'\:…. \\ $$ Answered by bemath last updated…

If-Cis-2pi-7-and-f-x-A-0-n-1-14-A-n-x-n-Then-prove-that-0-6-f-n-x-7-A-0-A-7-x-7-A-14-x-14-where-Cis-Cos-iSin-

Question Number 61835 by alphaprime last updated on 09/Jun/19 $$\mathrm{If}\:\alpha\:=\:\mathrm{Cis}\left(\mathrm{2}\pi/\mathrm{7}\right)\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{A}_{\mathrm{0}} \:+\:\sum_{\mathrm{n}=\mathrm{1}} ^{\mathrm{14}} \mathrm{A}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \: \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}\:\sum_{\alpha=\mathrm{0}} ^{\mathrm{6}} \mathrm{f}\left(\alpha^{\mathrm{n}} \mathrm{x}\right)=\:\mathrm{7}\left(\mathrm{A}_{\mathrm{0}} +\mathrm{A}_{\mathrm{7}} \mathrm{x}^{\mathrm{7}} +\mathrm{A}_{\mathrm{14}} \mathrm{x}^{\mathrm{14}} \right)…

If-a-Cos-iSin-and-b-Cos-iSin-Prove-that-a-b-1-ab-a-b-1-ab-Sin-Sin-Sin-Sin-

Question Number 61799 by alphaprime last updated on 08/Jun/19 $$\mathrm{If}\:\mathrm{a}\:=\:\mathrm{Cos}\alpha\:−\mathrm{iSin}\alpha\:\mathrm{and}\:\mathrm{b}\:=\:\mathrm{Cos}\beta\:−\mathrm{iSin}\beta \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\frac{\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{1}−\mathrm{ab}\right)}{\left(\mathrm{a}−\mathrm{b}\right)\left(\mathrm{1}+\mathrm{ab}\right)}\:=\:\frac{\mathrm{Sin}\alpha+\mathrm{Sin}\beta}{\mathrm{Sin}\alpha−\mathrm{Sin}\beta} \\ $$ Answered by tanmay last updated on 09/Jun/19 $${a}={e}^{−{i}\alpha} \:\:\:{b}={e}^{−{i}\beta} \\ $$$$\frac{{a}}{{b}}={e}^{−{i}\left(\propto−\beta\right)}…

Prove-it-sin-pi-2m-1-sin-2pi-2m-1-sin-mpi-2m-1-2m-1-2-m-

Question Number 127206 by MathSh last updated on 27/Dec/20 $${Prove}\:{it}: \\ $$$${sin}\frac{\pi}{\mathrm{2}{m}+\mathrm{1}}\centerdot{sin}\frac{\mathrm{2}\pi}{\mathrm{2}{m}+\mathrm{1}}\centerdot…\centerdot{sin}\frac{{m}\pi}{\mathrm{2}{m}+\mathrm{1}}=\frac{\sqrt{\mathrm{2}{m}+\mathrm{1}}}{\mathrm{2}^{{m}} } \\ $$ Answered by Olaf last updated on 28/Dec/20 $$ \\ $$$$\Omega\:=\:\underset{{k}=\mathrm{1}}…

Question-192733

Question Number 192733 by Mingma last updated on 25/May/23 Answered by MM42 last updated on 25/May/23 $$\frac{\mathrm{1}−\frac{\mathrm{2}{tanA}}{\mathrm{1}+{tan}^{\mathrm{2}} {A}}}{\mathrm{1}+\frac{\mathrm{1}−{tan}^{\mathrm{2}} {A}}{\mathrm{1}+{tan}^{\mathrm{2}} {A}}}={tanA}−\mathrm{1} \\ $$$$\frac{{tan}^{\mathrm{2}} {A}−\mathrm{2}{tanA}+\mathrm{1}}{\mathrm{2}}={tanA}−\mathrm{1} \\ $$$${tan}^{\mathrm{2}}…

If-1-cos-x-1-sin-x-3-2-then-1-cos-x-1-sin-x-nice-trigonometry-

Question Number 127169 by bramlexs22 last updated on 27/Dec/20 $${If}\:\left(\mathrm{1}+\mathrm{cos}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\:=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\:{then}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)\left(\mathrm{1}−\mathrm{sin}\:{x}\right)\:=? \\ $$$$ \\ $$$${nice}\:{trigonometry}\: \\ $$ Commented by Dwaipayan Shikari last updated on…