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Category: Trigonometry

If-and-satisfy-sin-cos-1-2-then-the-greatest-value-of-2cos-sin-

Question Number 27821 by bmind4860 last updated on 15/Jan/18 $${If}\:\alpha\:{and}\:\beta\:{satisfy}\:{sin}\alpha{cos}\beta=\:−\frac{\mathrm{1}}{\mathrm{2}}\:{then} \\ $$$${the}\:{greatest}\:{value}\:{of}\:\mathrm{2}{cos}\alpha{sin}\beta \\ $$ Answered by ajfour last updated on 15/Jan/18 $$\mathrm{sin}\:\alpha\mathrm{cos}\:\beta=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{2sin}\:\alpha\mathrm{cos}\:\beta=−\mathrm{1} \\…

If-A-B-0-pi-2-such-that-3sin-2-A-2sin-2-B-1-and-3sin2A-2sin2B-0-find-the-value-of-A-B-

Question Number 27820 by bmind4860 last updated on 15/Jan/18 $${If}\:{A},{B}\epsilon\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\right)\:{such}\:{that}\:\mathrm{3}{sin}^{\mathrm{2}} {A}+\mathrm{2}{sin}^{\mathrm{2}} {B}=\mathrm{1} \\ $$$${and}\:\mathrm{3}{sin}\mathrm{2}{A}−\mathrm{2}{sin}\mathrm{2}{B}=\mathrm{0},\:{find}\:{the}\:{value}\:{of}\:{A}+{B}. \\ $$ Answered by ajfour last updated on 15/Jan/18 $$\frac{\mathrm{3}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{A}\right)+\mathrm{1}−\mathrm{cos}\:\mathrm{2}{B}=\mathrm{1} \\…

3-cos-x-4-cos-y-3-sin-x-4sin-y-5-find-x-amp-y-with-acute-angle-

Question Number 93256 by i jagooll last updated on 12/May/20 $$\begin{cases}{\mathrm{3}\:\mathrm{cos}\:\mathrm{x}\:=\:\mathrm{4}\:\mathrm{cos}\:\mathrm{y}}\\{\mathrm{3}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{4sin}\:\mathrm{y}\:=\:\mathrm{5}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\&\mathrm{y}\:\mathrm{with}\:\mathrm{acute}\:\mathrm{angle}\: \\ $$ Commented by john santu last updated on 12/May/20 $$\begin{cases}{\mathrm{9}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:=\:\mathrm{16}\:\mathrm{cos}\:^{\mathrm{2}}…

the-number-of-x-0-2pi-for-which-2sin-4-x-18cos-2-x-2cos-4-x-18sin-2-x-1-

Question Number 27706 by shivamgiri last updated on 13/Jan/18 $${the}\:{number}\:{of}\:{x}\epsilon\left[\mathrm{0},\mathrm{2}\pi\right]{for}\:{which}\mid\sqrt{}\mathrm{2}{sin}^{\mathrm{4}\:} {x}+\mathrm{18}{cos}^{\mathrm{2}} {x}−\sqrt{\mathrm{2}{cos}^{\mathrm{4}} {x}+\mathrm{18}{sin}^{\mathrm{2}} {x}}\mid=\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-27640

Question Number 27640 by Tinkutara last updated on 11/Jan/18 Answered by ajfour last updated on 11/Jan/18 $$\mathrm{cos}\:{C}=\frac{\mathrm{3}}{\mathrm{5}}=\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}{ab}} \\ $$$$\Rightarrow\:\frac{\left({n}+\mathrm{1}\right)^{\mathrm{2}} +\left({n}+\mathrm{2}\right)^{\mathrm{2}} −{n}^{\mathrm{2}} }{\mathrm{2}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}=\frac{\mathrm{3}}{\mathrm{5}}…

Question-27605

Question Number 27605 by ajfour last updated on 10/Jan/18 Answered by mrW2 last updated on 13/Jan/18 $$\frac{{DB}}{{DC}}=\frac{{AB}}{{AC}}=\frac{{c}}{{b}} \\ $$$$\Rightarrow{DB}=\frac{{ac}}{{b}+{c}} \\ $$$$\Rightarrow{DC}=\frac{{ab}}{{b}+{c}} \\ $$$${AD}=\frac{\mathrm{2}\sqrt{{s}\left({s}−{a}\right){bc}}}{{b}+{c}} \\ $$$$\frac{{AE}}{{AB}}=\frac{{AD}}{{DB}}=\frac{\mathrm{2}\sqrt{{s}\left({s}−{a}\right){bc}}}{{b}+{c}}×\frac{{b}+{c}}{{ac}}=\frac{\mathrm{2}\sqrt{{s}\left({s}−{a}\right){bc}}}{{ac}}…

find-the-number-of-values-of-p-for-which-equation-sin-3-x-1-p-3-3p-sin-x-0-p-gt-0-has-a-root-

Question Number 158523 by gsk2684 last updated on 05/Nov/21 $${find}\:{the}\:{number}\:{of}\:{values}\:{of}\:{p} \\ $$$${for}\:{which}\:{equation}\: \\ $$$$\mathrm{sin}^{\mathrm{3}} {x}+\mathrm{1}+{p}^{\mathrm{3}} −\mathrm{3}{p}\:\mathrm{sin}\:{x}\:=\mathrm{0}\left({p}>\mathrm{0}\right) \\ $$$${has}\:{a}\:{root}? \\ $$ Answered by mr W last…