Question Number 152175 by john_santu last updated on 26/Aug/21 $$\mathrm{what}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{sin}\:\mathrm{2x}\:\mathrm{if}\:\mathrm{given} \\ $$$$\:\mathrm{cos}\:\mathrm{3x}\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}} \\ $$ Commented by MJS_new last updated on 26/Aug/21 $$\mathrm{cos}\:\mathrm{3}{x}\:=\mathrm{4cos}^{\mathrm{3}} \:{x}\:−\mathrm{3cos}\:{x} \\ $$$$\mathrm{sin}\:\mathrm{2}{x}\:=\pm\mathrm{2cos}\:{x}\:\sqrt{\mathrm{1}−\mathrm{cos}^{\mathrm{2}}…
ABC-is-an-isocel-triangle-such-as-AB-AC-3-and-BC-4-and-are-its-angles-Show-that-cos-2-sin-2-Hi-sirs-
Question Number 86614 by mathocean1 last updated on 29/Mar/20 $${ABC}\:{is}\:{an}\:{isocel}\:{triangle}\:{such}\:{as} \\ $$$${AB}={AC}=\mathrm{3}\:\:{and}\:{BC}=\mathrm{4} \\ $$$$\alpha\:,\:\beta\:,\:{and}\:\gamma\:{are}\:{its}\:{angles}. \\ $$$${Show}\:{that}\:{cos}\left(\frac{\alpha+\beta}{\mathrm{2}}\right)={sin}\left(\frac{\gamma}{\mathrm{2}}\right) \\ $$$${Hi}\:{sirs}… \\ $$ Answered by TANMAY PANACEA. last…
Question Number 21060 by NECx last updated on 11/Sep/17 $$\mathrm{write}\:\mathrm{sin}\:\mathrm{1}°\:\mathrm{in}\:\mathrm{surd}\:\mathrm{form} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{workings}. \\ $$ Commented by NECx last updated on 11/Sep/17…
Question Number 21050 by Tinkutara last updated on 10/Sep/17 $$\mathrm{The}\:\mathrm{most}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{sin}{x}\:+\:\mathrm{cos}{x}\:=\:\underset{{a}\in{R}} {\mathrm{min}}\left\{\mathrm{1},\:{a}^{\mathrm{2}} \:−\:\mathrm{4}{a}\:+\:\mathrm{6}\right\} \\ $$$$\mathrm{is} \\ $$ Answered by mrW1 last updated on 11/Sep/17…
Question Number 86550 by DuDono last updated on 29/Mar/20 $$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{tan}\:^{−\mathrm{1}} {x}=\frac{\mathrm{ln}\:\left(−{x}^{\mathrm{2}} +\mathrm{2}{ix}+\mathrm{1}\right)−\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{\mathrm{2}{i}} \\ $$ Commented by john santu last updated on 29/Mar/20…
Question Number 86540 by jagoll last updated on 29/Mar/20 $$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{cos}\:\left(\frac{\mathrm{A}}{\mathrm{2}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{B}}{\mathrm{2}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{C}}{\mathrm{2}}\right)\:=\: \\ $$$$\mathrm{4}\:\mathrm{cos}\:\left(\frac{\pi+\mathrm{A}}{\mathrm{4}}\right)\mathrm{cos}\:\left(\frac{\pi+\mathrm{B}}{\mathrm{4}}\right)\mathrm{cos}\:\left(\frac{\pi−\mathrm{C}}{\mathrm{4}}\right) \\ $$$$\mathrm{where}\:\mathrm{A}+\mathrm{B}+\mathrm{C}\:=\:\pi \\ $$ Commented by jagoll last updated on 29/Mar/20…
Question Number 152035 by puissant last updated on 25/Aug/21 $${Show}\:{that}\:\mathrm{2}{sin}\mathrm{7}\theta{cos}\mathrm{3}\theta={sin}\mathrm{10}\theta+{sin}\mathrm{4}\theta. \\ $$ Answered by som(math1967) last updated on 25/Aug/21 $$\mathrm{2}{sinA}\boldsymbol{{cosB}}=\boldsymbol{{sin}}\left(\boldsymbol{{A}}+\boldsymbol{{B}}\right)+\boldsymbol{{sin}}\left(\boldsymbol{{A}}−\boldsymbol{{B}}\right) \\ $$$$\therefore\mathrm{2}\boldsymbol{{sin}}\mathrm{7}\boldsymbol{\theta{cos}}\mathrm{3}\boldsymbol{\theta}=\boldsymbol{{sin}}\left(\mathrm{7}\boldsymbol{\theta}+\mathrm{3}\boldsymbol{\theta}\right)+\boldsymbol{{sin}}\left(\mathrm{7}\boldsymbol{\theta}−\mathrm{3}\boldsymbol{\theta}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\boldsymbol{{sin}}\mathrm{10}\boldsymbol{\theta}+{s}\boldsymbol{{in}}\mathrm{4}\boldsymbol{\theta} \\…
Question Number 86486 by jagoll last updated on 29/Mar/20 $$\mathrm{If}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}}\:=\:? \\ $$ Commented by john santu last updated on 29/Mar/20 $$\Rightarrow\:\frac{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}\:=\:\left(\mathrm{i}\right) \\ $$$$\Rightarrow\:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}}…
Question Number 86476 by DuDono last updated on 28/Mar/20 $$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{sin}^{−\mathrm{1}} \alpha=−{i}\:\mathrm{ln}\:\left(\alpha\pm\sqrt{\alpha^{\mathrm{2}} −\mathrm{1}}\right)−\frac{\pi}{\mathrm{2}} \\ $$ Commented by MJS last updated on 28/Mar/20 $$\mathrm{the}\:\mathrm{path}\:\mathrm{is}\:\mathrm{this}: \\…
Question Number 152010 by RB95 last updated on 25/Aug/21 Commented by RB95 last updated on 25/Aug/21 $$ \\ $$$${Slt} \\ $$$${Pouviez}\:{vous}\:{m}'{aider}? \\ $$ Answered by…