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Category: Trigonometry

In-any-ABC-a-b-cos-C-c-cos-B-

Question Number 21431 by Tinkutara last updated on 23/Sep/17 $$\mathrm{In}\:\mathrm{any}\:\Delta{ABC},\:{a}\left({b}\:\mathrm{cos}\:{C}\:−\:{c}\:\mathrm{cos}\:{B}\right)\:= \\ $$ Answered by $@ty@m last updated on 23/Sep/17 $$={ab}\mathrm{cos}\:{C}−{ac}\mathrm{cos}\:{B} \\ $$$$=\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}}−\frac{{c}^{\mathrm{2}}…

In-any-ABC-a-2-sin-B-sin-C-

Question Number 21429 by Tinkutara last updated on 23/Sep/17 $$\mathrm{In}\:\mathrm{any}\:\Delta{ABC},\:\Sigma{a}^{\mathrm{2}} \left(\mathrm{sin}\:{B}\:−\:\mathrm{sin}\:{C}\right)\:= \\ $$ Answered by $@ty@m last updated on 23/Sep/17 $${We}\:{have} \\ $$$$\frac{{a}}{\mathrm{sin}\:{A}}=\frac{{b}}{\mathrm{sin}\:{B}}=\frac{{c}}{\mathrm{sin}\:{C}}={k},\:{say} \\ $$$$\therefore\Sigma{a}^{\mathrm{2}}…

In-any-ABC-the-value-of-2ac-sin-A-B-C-2-is-

Question Number 21430 by Tinkutara last updated on 23/Sep/17 $$\mathrm{In}\:\mathrm{any}\:\Delta{ABC},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{2}{ac}\:\mathrm{sin}\:\left(\frac{{A}\:−\:{B}\:+\:{C}}{\mathrm{2}}\right)\:\mathrm{is} \\ $$ Answered by $@ty@m last updated on 23/Sep/17 $$=\mathrm{2}{ac}\mathrm{sin}\:\left(\frac{\pi−\mathrm{2}{B}}{\mathrm{2}}\right) \\ $$$$=\mathrm{2}{ac}\mathrm{cos}\:{B} \\…

If-sin-10-x-cos-10-x-11-36-find-sin-12-x-cos-12-x-

Question Number 86878 by jagoll last updated on 01/Apr/20 $$\mathrm{If}\:\mathrm{sin}\:^{\mathrm{10}} \:\left(\mathrm{x}\right)\:+\:\mathrm{cos}\:^{\mathrm{10}} \:\left(\mathrm{x}\right)\:=\:\frac{\mathrm{11}}{\mathrm{36}} \\ $$$$\mathrm{find}\:\mathrm{sin}\:^{\mathrm{12}} \:\left(\mathrm{x}\right)\:+\:\mathrm{cos}\:\:^{\mathrm{12}} \left(\mathrm{x}\right)\:=\:? \\ $$ Commented by Prithwish Sen 1 last updated…

Question-21297

Question Number 21297 by NECx last updated on 19/Sep/17 Answered by sma3l2996 last updated on 20/Sep/17 $$\mathrm{2}{sin}^{−\mathrm{1}} \left({x}\sqrt{\mathrm{6}}\right)+{sin}^{−\mathrm{1}} \left(\mathrm{4}{x}\right)=\frac{\pi}{\mathrm{2}} \\ $$$${sin}^{−\mathrm{1}} \left(\mathrm{4}{x}\right)=\frac{\pi}{\mathrm{2}}−\mathrm{2}{sin}^{−\mathrm{1}} \left({x}\sqrt{\mathrm{6}}\right) \\ $$$${sin}\left({sin}^{−\mathrm{1}}…

Question-21296

Question Number 21296 by NECx last updated on 19/Sep/17 Commented by NECx last updated on 19/Sep/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{this}.\:\mathrm{It}\:\mathrm{was} \\ $$$$\mathrm{solved}\:\mathrm{before}\:\mathrm{but}\:\mathrm{i}\:\mathrm{cant}\:\mathrm{assess}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{again}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}…

Let-pi-pi-be-such-that-cos-1-and-cos-1-e-The-number-of-pairs-of-satisfying-the-above-system-of-equation-is-

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…