Question Number 144329 by gsk2684 last updated on 24/Jun/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\: \\ $$$$\mathrm{of}\:\sqrt{\mathrm{6}−\mathrm{cos}\:\mathrm{x}+\mathrm{7sin}^{\mathrm{2}} \mathrm{x}}+\mathrm{cos}\:\mathrm{x}=\mathrm{0} \\ $$ Commented by MJS_new last updated on 25/Jun/21 $$\mathrm{let}\:{c}=\mathrm{cos}\:{x}\:\Rightarrow\:−\mathrm{1}\leqslant{c}\leqslant\mathrm{1} \\ $$$$\sqrt{\mathrm{13}−{c}−\mathrm{7}{c}^{\mathrm{2}}…
Question Number 13249 by Tinkutara last updated on 17/May/17 $$\mathrm{If}\:{m}\mathrm{sin}\theta\:=\:{n}\mathrm{sin}\left(\theta\:+\:\mathrm{2}\alpha\right),\:\mathrm{then} \\ $$$$\mathrm{tan}\left(\theta\:+\:\alpha\right)\mathrm{cot}\alpha\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left[\mathrm{Answer}\:\mathrm{given}\:\mathrm{in}\:\mathrm{my}\:\mathrm{book}\:\mathrm{is}\:\frac{\mathrm{1}\:−\:{n}}{\mathrm{1}\:+\:{n}}\right] \\ $$ Commented by prakash jain last updated on 17/May/17 $$\mathrm{tan}\:\left(\theta+\alpha\right)\mathrm{cot}\:\alpha…
Question Number 78785 by jagoll last updated on 20/Jan/20 $$ \\ $$$$ \\ $$$$\left(\mathrm{1}+\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\right)^{\mathrm{3}−\mathrm{cos}\:\mathrm{2x}} =\:\left(\mathrm{sin}\:\frac{\pi}{\mathrm{14}}+\mathrm{cos}\:\frac{\pi}{\mathrm{14}}\right)^{\mathrm{10}\:\mathrm{sin}\:\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{solution} \\ $$ Answered by john santu last updated…
Question Number 144305 by gsk2684 last updated on 24/Jun/21 $$\mathrm{if}\:\left(\mathrm{a}−\mathrm{b}\right)\mathrm{sin}\left(\theta+\phi\right)=\left(\mathrm{a}+\mathrm{b}\right)\mathrm{sin}\left(\theta−\phi\right)\: \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{tan}\frac{\theta}{\mathrm{2}}\:−\:\mathrm{b}\:\mathrm{tan}\frac{\phi}{\mathrm{2}}\:=\:\mathrm{c}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following} \\ $$$$\left.\mathrm{i}\right)\:\mathrm{sin}\phi\:=\:\frac{\mathrm{2bc}}{\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{c}^{\mathrm{2}} }\: \\ $$$$\left.\mathrm{ii}\right)\:\mathrm{sin}\theta\:=\:\frac{\mathrm{2ac}}{\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} }\: \\…
Question Number 13234 by tawa tawa last updated on 17/May/17 $$\mathrm{The}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{elevation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sun}\:\mathrm{is}\:\mathrm{27}°.\:\:\mathrm{A}\:\mathrm{man}\:\mathrm{is}\:\mathrm{180}\:\mathrm{cm}\:\mathrm{tall}\:.\:\mathrm{How}\:\mathrm{long}\:\mathrm{is} \\ $$$$\mathrm{his}\:\mathrm{shadow}.\:\mathrm{Give}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\:\mathrm{10cm} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 17/May/17 $${l}=\mathrm{180}.{tg}\mathrm{27}^{°} #\mathrm{90}\:{cm} \\…
Question Number 78767 by jagoll last updated on 20/Jan/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x} \\ $$ Commented by mr W last updated on 20/Jan/20 $${since}\:\mathrm{cos}^{\mathrm{4}} \:{x}\geqslant\mathrm{0},…
Question Number 13224 by Tinkutara last updated on 16/May/17 Commented by Tinku Tara last updated on 16/May/17 $$\mathrm{Can}\:\mathrm{u}\:\mathrm{please}\:\mathrm{use}\:\mathrm{a}\:\mathrm{different}\:\mathrm{name} \\ $$$$\mathrm{for}\:\mathrm{your}\:\mathrm{user}\:\mathrm{id}.\:\mathrm{Since}\:\mathrm{tinku}\:\mathrm{tara} \\ $$$$\mathrm{is}\:\mathrm{publisher}\:\mathrm{name}. \\ $$$$\mathrm{Thank}\:\mathrm{You}\:\mathrm{for}\:\mathrm{ur}\:\mathrm{cooperation}. \\…
Question Number 13201 by Tinkutara last updated on 16/May/17 $$\mathrm{In}\:\mathrm{a}\:\Delta{ABC}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{sin}\:{A}\:+\:\mathrm{sin}\:\mathrm{B}}{\mathrm{2}}\:\leqslant\:\mathrm{sin}\:\left(\frac{{A}\:+\:{B}}{\mathrm{2}}\right) \\ $$ Commented by ajfour last updated on 16/May/17 $${kindly}\:{check}\:{if} \\ $$$${B}=\mathrm{0}\:{and}\:{A}=−\frac{\pi}{\mathrm{3}}\:. \\…
Question Number 13194 by Tinkutara last updated on 16/May/17 Answered by ajfour last updated on 16/May/17 $$\left({i}\right)\: \\ $$$$\:{let}\:\:{x}=\mathrm{tan}\:\alpha\:,\:{y}=\mathrm{tan}\:\beta\:,\:{z}=\mathrm{tan}\:\gamma \\ $$$$\mathrm{tan}\:\left(\alpha+\beta+\gamma\right)=\frac{\Sigma\mathrm{tan}\:\alpha−\Pi\mathrm{tan}\:\alpha}{\mathrm{1}−\Sigma\mathrm{tan}\:\alpha\:\mathrm{tan}\:\beta} \\ $$$${x}+{y}+{z}\:=\:{xyz}\:\:\:\:\:….\:\left(\:{given}\right) \\ $$$$\:\Rightarrow\:\Sigma\mathrm{tan}\:\alpha\:=\:\Pi\mathrm{tan}\:\alpha\:\:\:\:\:\:\:…
Question Number 78709 by jagoll last updated on 20/Jan/20 $$\mathrm{if}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{1} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{cos}\:^{\mathrm{12}} \mathrm{x}+\mathrm{3cos}\:^{\mathrm{10}} \mathrm{x}+\mathrm{3cos}\:^{\mathrm{8}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x} \\ $$ Commented by jagoll last updated on…