Question Number 135795 by benjo_mathlover last updated on 16/Mar/21 $${What}\:{the}\:{value}\:{of}\:\left(\mathrm{1}−\mathrm{cot}\:\mathrm{23}°\right)\left(\mathrm{1}−\mathrm{cot}\:\mathrm{22}°\right). \\ $$ Answered by MJS_new last updated on 16/Mar/21 $$\left(\mathrm{1}−\mathrm{cot}\:\left(\frac{\mathrm{45}}{\mathrm{2}}−{x}\right)\right)\left(\mathrm{1}−\mathrm{cot}\:\left(\frac{\mathrm{45}}{\mathrm{2}}+{x}\right)\right)=\mathrm{2} \\ $$ Answered by liberty…
Question Number 135791 by benjo_mathlover last updated on 16/Mar/21 $${If}\:{x}^{\mathrm{2}} +\left(\mathrm{tan}\:\theta+\mathrm{cot}\:\theta\right){x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$${has}\:{two}\:{real}\:{solutions}\: \\ $$$$\left\{\:\mathrm{2}−\sqrt{\mathrm{3}}\:,\:\mathrm{2}+\sqrt{\mathrm{3}}\:\right\},\:{find}\:\begin{cases}{\mathrm{sin}\:\theta}\\{\mathrm{cos}\:\theta}\end{cases}\:. \\ $$ Answered by EDWIN88 last updated on 17/Mar/21 $$\mathrm{By}\:\mathrm{Vieta}'\mathrm{s}\:\Rightarrow\:\mathrm{x}_{\mathrm{1}}…
Question Number 135679 by liberty last updated on 15/Mar/21 $$\left(\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\right)\left(\mathrm{2tan}\:{x}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}}\right)+\mathrm{2}\:=\:\mathrm{0} \\ $$ Answered by EDWIN88 last updated on 15/Mar/21 $$\mathrm{Let}\:\mathrm{tan}\:\frac{\mathrm{x}}{\mathrm{2}}\:=\:\mathrm{t}\:\rightarrow\begin{cases}{\mathrm{cos}\:\mathrm{x}=\frac{\mathrm{1}−\mathrm{t}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }}\\{\mathrm{sin}\:\mathrm{x}=\frac{\mathrm{2t}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }}\\{\mathrm{tan}\:\mathrm{x}=\frac{\mathrm{2t}}{\mathrm{1}−\mathrm{t}^{\mathrm{2}} }}\end{cases} \\ $$$$\Leftrightarrow\:\left(\frac{\mathrm{1}−\mathrm{t}^{\mathrm{2}}…
Question Number 4600 by Yozzii last updated on 11/Feb/16 $${Find}\:{the}\:{value}\:{of}\:{S}\:{where}\:{S}=\underset{{r}=\mathrm{1}} {\overset{\mathrm{89}} {\sum}}{sin}^{\mathrm{6}} {r}°. \\ $$ Commented by FilupSmith last updated on 11/Feb/16 $$\mathrm{Don}'\mathrm{t}\:\mathrm{you}\:\mathrm{use}\:\mathrm{the}\:\mathrm{series}\:\mathrm{representation} \\ $$$$\mathrm{for}\:\mathrm{sine}?…
Question Number 135604 by liberty last updated on 14/Mar/21 $$\:\frac{\mathrm{sin}\:\left(\pi/\mathrm{7}\right).\mathrm{cos}\:\left(\pi/\mathrm{14}\right)}{\mathrm{tan}\:\left(\mathrm{3}\pi/\mathrm{14}\right)\left(\mathrm{2cos}\:\left(\pi/\mathrm{7}\right)−\mathrm{1}\right)}\:=? \\ $$ Answered by EDWIN88 last updated on 14/Mar/21 $$\:\mathrm{Remark}\:\begin{cases}{\mathrm{sin}\:\mathrm{3x}=\mathrm{3sin}\:\mathrm{x}−\mathrm{4sin}\:^{\mathrm{3}} \mathrm{x}}\\{\mathrm{cos}\:\mathrm{3x}=\mathrm{4cos}\:^{\mathrm{3}} \mathrm{x}−\mathrm{3cos}\:\mathrm{x}}\end{cases} \\ $$$$\mathrm{let}\:\mathrm{x}\:=\:\frac{\pi}{\mathrm{14}}\:\Rightarrow\frac{\mathrm{sin}\:\left(\pi/\mathrm{7}\right)\mathrm{cos}\:\left(\pi/\mathrm{14}\right)}{\mathrm{tan}\:\left(\mathrm{3}\pi/\mathrm{14}\right)\left(\mathrm{2cos}\:\left(\pi/\mathrm{7}\right)−\mathrm{1}\right)}\: \\…
Question Number 135603 by liberty last updated on 14/Mar/21 $$\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{17}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{17}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{8}\pi}{\mathrm{17}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{16}\pi}{\mathrm{17}}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 70052 by ahmadshahhimat775@gmail.com last updated on 30/Sep/19 $$ \\ $$$$\mathrm{sin}\:{A}+\mathrm{sin}\:{B}={n}\:\:\:\:\:\:\:\:\:{and}\:\:\:\:\:\:\:\:\mathrm{cos}\:{A}+\mathrm{cos}\:{B}={m} \\ $$$$\mathrm{sin}\:\left({A}+{B}\right)=? \\ $$ Answered by $@ty@m123 last updated on 30/Sep/19 $$\mathrm{sin}\:{A}+\mathrm{sin}\:{B}={n} \\…
Question Number 135594 by liberty last updated on 14/Mar/21 $${Trigonometry} \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{sin}\:\mathrm{2}{x}+\mathrm{5}\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)+\mathrm{1}\:=\:\mathrm{0} \\ $$$$\:{find}\:{the}\:{solution} \\ $$ Answered by EDWIN88 last updated on 14/Mar/21…
Question Number 4429 by alib last updated on 24/Jan/16 $$\left({sin}\:{x}\:+\sqrt{\mathrm{3}}\:{cos}\:{x}\right)\:{sin}\:\mathrm{3}{x}\:=\:\mathrm{2} \\ $$ Answered by Yozzii last updated on 24/Jan/16 $${sinx}+\sqrt{\mathrm{3}}{cosx}=\sqrt{\mathrm{1}+\mathrm{3}}{sin}\left({x}+\pi/\mathrm{3}\right) \\ $$$$=\mathrm{2}{sin}\left({x}+\frac{\pi}{\mathrm{3}}\right) \\ $$$$\left({sinx}+\sqrt{\mathrm{3}}{cosx}\right){sin}\mathrm{3}{x}=\mathrm{2}………\left(\Upsilon\right) \\…
Question Number 135497 by EDWIN88 last updated on 13/Mar/21 $$\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}+\frac{\pi}{\mathrm{4}}\right)\:=\:\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}−\frac{\pi}{\mathrm{4}}\right)+\:\sqrt{\mathrm{7}}\:\mathrm{cos}\:\mathrm{x} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\Leftrightarrow\:\mathrm{sin}\:^{\mathrm{2}} \left({x}+\frac{\pi}{\mathrm{4}}\right)−\mathrm{sin}\:^{\mathrm{2}} \left({x}−\frac{\pi}{\mathrm{4}}\right)=\sqrt{\mathrm{7}}\:\mathrm{cos}\:{x} \\…