Question Number 17421 by Tinkutara last updated on 05/Jul/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{2}^{\mid{x}\mid} \:=\:\mathrm{1}\:+\:\mathrm{2}\mid\mathrm{cos}\:{x}\mid\:\mathrm{is} \\ $$ Answered by mrW1 last updated on 05/Jul/17 $$\mathrm{1}\leqslant\:\mathrm{1}\:+\:\mathrm{2}\mid\mathrm{cos}\:{x}\mid\:\leqslant\mathrm{3} \\ $$$$\mathrm{1}\leqslant\:\mathrm{2}^{\mid\mathrm{x}\mid}…
Question Number 17420 by sushmitak last updated on 05/Jul/17 $$\mathrm{tan}^{\mathrm{6}} \frac{\pi}{\mathrm{9}}−\mathrm{33tan}^{\mathrm{4}} \frac{\pi}{\mathrm{9}}+\mathrm{27tan}^{\mathrm{2}} \frac{\pi}{\mathrm{9}}=? \\ $$ Answered by Tinkutara last updated on 05/Jul/17 $$\mathrm{tan}\:\mathrm{3}\left(\frac{\pi}{\mathrm{9}}\right)\:=\:\sqrt{\mathrm{3}} \\ $$$$\sqrt{\mathrm{3}}\:=\:\frac{\mathrm{3}\:\mathrm{tan}\:\frac{\pi}{\mathrm{9}}\:−\:\mathrm{tan}^{\mathrm{3}}…
Question Number 82944 by jagoll last updated on 26/Feb/20 $$ \\ $$$$\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{27}^{\mathrm{o}} \right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{87}^{\mathrm{o}} \right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{33}^{\mathrm{o}} \right)\:= \\ $$ Commented by john santu last…
Question Number 17348 by Tinkutara last updated on 04/Jul/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{points}\:\mathrm{in}\:\left(−\infty,\:\infty\right)\:\mathrm{for} \\ $$$$\mathrm{which}\:{x}^{\mathrm{2}} \:−\:{x}\:\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\:=\:\mathrm{0}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{2} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{0} \\ $$ Answered by…
Question Number 82879 by jagoll last updated on 25/Feb/20 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{cos}\:^{\mathrm{2}} \mathrm{a}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{b}}{\mathrm{sin}\:\mathrm{acos}\:\mathrm{a}\:+\:\mathrm{sin}\:\mathrm{bcos}\:\mathrm{b}}\:=\:\mathrm{cot}\:\left(\mathrm{a}+\mathrm{b}\right) \\ $$ Commented by mahdi last updated on 25/Feb/20 $$\mathrm{problem}: \\…
Question Number 148381 by liberty last updated on 27/Jul/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 17233 by sushmitak last updated on 02/Jul/17 $$\mathrm{How}\:\mathrm{to}\:\mathrm{find}\:\mathrm{out}\:\mathrm{if} \\ $$$$\mathrm{cos}\:\left(\mathrm{cos}\:{x}\right)>\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right) \\ $$$$\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)>\mathrm{sin}\:\left(\mathrm{cos}\:{x}\right) \\ $$$$\mathrm{cos}\:\left(\mathrm{sin}\:\left(\mathrm{cos}\:{x}\right)\right)>\mathrm{sin}\:\left(\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\right) \\ $$$$\mathrm{cos}\:\left(\mathrm{cos}\:\left(\mathrm{cos}\:{x}\right)\right)>\mathrm{sin}\:\left(\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)\right) \\ $$$$\mathrm{exam}\:\mathrm{questions}. \\ $$$$\mathrm{calculators}\:\mathrm{not}\:\mathrm{allowed}. \\ $$ Commented…
Question Number 82767 by jagoll last updated on 24/Feb/20 $$\mathrm{If}\:\frac{\mathrm{sin}\:\left(\mathrm{A}+\theta\right)}{\mathrm{sin}\:\left({B}+\theta\right)}\:=\:\sqrt{\frac{\mathrm{sin}\:\mathrm{2}{A}}{\mathrm{sin}\:\mathrm{2}{B}}} \\ $$$${prove}\:{that}\:\mathrm{tan}\:^{\mathrm{2}} \theta\:=\:\mathrm{tan}\:{A}.\mathrm{tan}\:{B} \\ $$ Commented by jagoll last updated on 24/Feb/20 $${thank}\:{you}\:{mr}\:{w}\:{and}\:{john} \\ $$…
Question Number 82759 by jagoll last updated on 24/Feb/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2cos}\:\mathrm{80}^{{o}} }}}}\:=\: \\ $$ Answered by jagoll last updated on 24/Feb/20 Terms of Service…
Question Number 17153 by Tinkutara last updated on 01/Jul/17 $$\mathrm{If}\:{m},\:{n}\:\in\:{N}\left({n}\:>\:{m}\right),\:\mathrm{then}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${n}\mid\mathrm{sin}\:{x}\mid\:=\:{m}\mid\mathrm{sin}\:{x}\mid\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{2}\pi\right]\:\mathrm{is} \\ $$ Answered by mrW1 last updated on 01/Jul/17 $${n}\mid\mathrm{sin}\:{x}\mid\:=\:{m}\mid\mathrm{sin}\:{x}\mid \\…