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…
Question Number 151959 by john_santu last updated on 24/Aug/21 Answered by iloveisrael last updated on 24/Aug/21 $$\left(\mathrm{sin}\:^{\mathrm{2}} {x}\right)^{\mathrm{3}} +\left(\mathrm{cos}\:^{\mathrm{2}} {x}\right)^{\mathrm{3}} =\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\Rightarrow\left(\mathrm{1}\right)\left(\mathrm{sin}\:^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}−\left(\mathrm{sin}\:{x}\mathrm{cos}\:{x}\right)^{\mathrm{2}}…
Question Number 20886 by tammi last updated on 06/Sep/17 $${if}\:\mathrm{sin}\:{x}={m}\mathrm{sin}\:{y} \\ $$$${so}\:{proof}\:{that} \\ $$$$\mathrm{tan}\:\frac{\mathrm{1}}{\mathrm{2}}\left({x}−{y}\right)=\frac{{m}−\mathrm{1}}{{m}+\mathrm{1}}\mathrm{tan}\:\frac{\mathrm{1}}{\mathrm{2}}\left({x}+{y}\right) \\ $$ Answered by ajfour last updated on 06/Sep/17 $${m}=\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{y}}\:\:\:\:\Rightarrow\:\:\frac{{m}−\mathrm{1}}{{m}+\mathrm{1}}=\frac{\mathrm{sin}\:{x}−\mathrm{sin}\:{y}}{\mathrm{sin}\:{x}+\mathrm{sin}\:{y}} \\…
Question Number 20885 by tammi last updated on 06/Sep/17 $${if}\:\left(\theta−\varphi\right){subtle}\:{and}\:\:\:\mathrm{sin}\:\theta+\mathrm{sin}\:\varphi= \\ $$$$\left(\mathrm{cos}\:\varphi−\mathrm{cos}\:\theta\right)\sqrt{\mathrm{3}} \\ $$$${so}\:{proof}\:\mathrm{sin}\:\mathrm{3}\theta+\mathrm{sin}\:\mathrm{3}\varphi=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20884 by tammi last updated on 06/Sep/17 $$\mathrm{2cos}\:\frac{\pi}{\mathrm{3}}\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{13}}+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{13}}+\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{13}}=\mathrm{0} \\ $$ Answered by ajfour last updated on 06/Sep/17 $${must}\:{start}\:{with}\:\:\:\:\mathrm{2cos}\:\frac{\pi}{\mathrm{13}}…,\:{Then} \\ $$$$\:{L}.{H}.{S}.\:=\:\mathrm{cos}\:\left(\frac{\mathrm{10}\pi}{\mathrm{13}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{8}\pi}{\mathrm{13}}\right)+ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{13}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{13}}\right) \\…
Question Number 151941 by john_santu last updated on 24/Aug/21 $$\mathrm{Find}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\:\mathrm{6cos}\:\mathrm{x}−\mathrm{8sin}\:\mathrm{x}=\mathrm{5}\sqrt{\mathrm{3}} \\ $$$$\:\mathrm{0}°\leqslant\mathrm{x}\leqslant\mathrm{360}° \\ $$ Answered by iloveisrael last updated on 24/Aug/21 $$\:\Leftrightarrow\:\mathrm{3cos}\:{x}−\mathrm{4sin}\:{x}\:=\:\frac{\mathrm{5}\sqrt{\mathrm{3}}}{\mathrm{2}} \\…
Question Number 151922 by john_santu last updated on 24/Aug/21 $$\:\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\:+\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}}−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\pi}{\mathrm{9}}}\:=? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com