Question Number 21273 by 8116417733 last updated on 18/Sep/17 $$\mathrm{cos}\:\mathrm{70}+\mathrm{4cos}\:\mathrm{70} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21272 by Tinkutara last updated on 18/Sep/17 $$\mathrm{Let}\:\alpha,\:\beta\:\in\:\left(−\pi,\:\pi\right)\:\mathrm{be}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{cos}\left(\alpha\:−\:\beta\right)\:=\:\mathrm{1}\:\mathrm{and}\:\mathrm{cos}\left(\alpha\:+\:\beta\right)\:=\:\frac{\mathrm{1}}{{e}}. \\ $$$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{pairs}\:\mathrm{of}\:\alpha,\:\beta\:\mathrm{satisfying} \\ $$$$\mathrm{the}\:\mathrm{above}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\:\mathrm{is} \\ $$ Answered by mrW1 last updated on 18/Sep/17…
Question Number 21268 by oyshi last updated on 18/Sep/17 $${if}\:{A}+{B}+{C}=\pi \\ $$$${so}\:{proof}\: \\ $$$$\mathrm{sin}\:{A}+\mathrm{sin}\:{B}+\mathrm{sin}\:{C}=\mathrm{4cos}\:\frac{{A}}{\mathrm{2}}\mathrm{cos}\:\frac{{B}}{\mathrm{2}}\mathrm{cos}\:\frac{{C}}{\mathrm{2}} \\ $$ Answered by myintkhaing last updated on 18/Sep/17 $$\mathrm{L}.\mathrm{H}.\mathrm{S}=\:\mathrm{sin}\:\mathrm{A}+\mathrm{sin}\:\mathrm{B}+\mathrm{sin}\:\mathrm{C} \\…
Question Number 21267 by oyshi last updated on 18/Sep/17 $$\mathrm{cos}\:{A}+\mathrm{cos}\:{B}+\mathrm{cos}\:{C}=\mathrm{1}+\frac{{r}}{{R}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21266 by oyshi last updated on 18/Sep/17 $$\frac{{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{tan}\:{A}}+\frac{{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{tan}\:{B}}+\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{tan}\:{C}}=\mathrm{0} \\ $$ Answered by myintkhaing last updated on 18/Sep/17…
Question Number 21260 by oyshi last updated on 17/Sep/17 $${if}\:\left(\theta−\varphi\right)\:{subtle}\:{and}\:\mathrm{sin}\:\theta+\mathrm{sin}\:\varphi=\sqrt{\mathrm{3}\left(\mathrm{cos}\:\varphi\right.} \\ $$$$\left.−\mathrm{cos}\:\theta\right) \\ $$$${so}\:{proof}\:\mathrm{sin}\:\mathrm{3}\theta+\mathrm{sin}\:\mathrm{3}\varphi=\mathrm{0} \\ $$ Answered by 951172235v last updated on 07/Feb/19 $$\mathrm{sin}\:\theta+\mathrm{sin}\:\varphi\:=\sqrt{\mathrm{3}}\:\left(\mathrm{cos}\:\varphi−\mathrm{cos}\:\theta\right) \\…
Question Number 21259 by oyshi last updated on 17/Sep/17 $$\mathrm{2cos}\:\frac{\pi}{\mathrm{13}}\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} \\ $$ Answered by myintkhaing last updated on 18/Sep/17 $$\mathrm{L}.\mathrm{H}.\mathrm{S}=\mathrm{cos}\:\frac{\mathrm{10}\pi}{\mathrm{13}}\:+\mathrm{cos}\:\frac{\mathrm{8}\pi}{\mathrm{13}}\:+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{13}}\:+\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{13}} \\ $$$$=\mathrm{cos}\left(\pi−\frac{\mathrm{3}\pi}{\mathrm{13}}\right)+\mathrm{cos}\left(\pi−\frac{\mathrm{5}\pi}{\mathrm{13}}\right)+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{13}}+\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{13}} \\ $$$$=\:−\mathrm{cos}\frac{\mathrm{3}\pi}{\mathrm{13}}−\mathrm{cos}\frac{\mathrm{5}\pi}{\mathrm{13}}+\mathrm{cos}\frac{\mathrm{3}\pi}{\mathrm{13}}+\mathrm{cos}\frac{\mathrm{5}\pi}{\mathrm{13}}\:=\:\mathrm{0} \\…
Question Number 21241 by tawa tawa last updated on 17/Sep/17 $$\mathrm{Find}\:\mathrm{y}\:\mathrm{in}\:\mathrm{3rd}\:\mathrm{quadrant} \\ $$$$\mathrm{tan}\left(\mathrm{y}\:−\:\mathrm{30}\right)\:=\:\mathrm{cot}\left(\mathrm{y}\right) \\ $$ Answered by sma3l2996 last updated on 17/Sep/17 $${tan}\left({y}−\mathrm{30}\right)={cot}\left({y}\right) \\ $$$${tan}\left({y}−\mathrm{30}\right)=\frac{\mathrm{1}}{{tan}\left({y}\right)}\Leftrightarrow\frac{{tan}\left({y}\right)−{tan}\left(\mathrm{30}\right)}{\mathrm{1}+{tan}\left({y}\right){tan}\left(\mathrm{30}\right)}=\frac{\mathrm{1}}{{tany}}…
Question Number 86726 by A8;15: last updated on 30/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86716 by john santu last updated on 30/Mar/20 $$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{17}}\right)×\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)\:= \\ $$ Commented by jagoll last updated on 30/Mar/20 $$\frac{\mathrm{cos}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{4x}\:\mathrm{cos}\:\mathrm{8x}}{\mathrm{2sin}\:\mathrm{x}}\:×\:\mathrm{2sin}\:\mathrm{x}\:\: \\ $$$$\frac{\mathrm{sin}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{4x}\:\mathrm{cos}\:\mathrm{8x}}{\mathrm{2sin}\:\mathrm{x}}\:=\: \\ $$$$\frac{\mathrm{sin}\:\mathrm{4x}\:\mathrm{cos}\:\mathrm{4x}\:\mathrm{cos}\:\mathrm{8x}}{\mathrm{4sin}\:\mathrm{x}}\:=\:…