Question Number 158354 by cortano last updated on 03/Nov/21 $$\:\sqrt{\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}+{x}\right)}\:+\sqrt{\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right)}\:=\sqrt[{\mathrm{4}}]{\mathrm{2cos}\:\mathrm{2}{x}} \\ $$ Commented by tounghoungko last updated on 03/Nov/21 $$\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}+{x}\right)+\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right)+\mathrm{2}\sqrt{\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}+{x}\right)\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right)}=\sqrt{\mathrm{2cos}\:\mathrm{2}{x}} \\ $$$$\left({i}\right)\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}+{x}\right)+\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right)=\mathrm{2sin}\:\frac{\pi}{\mathrm{4}}\mathrm{cos}\:{x}=\sqrt{\mathrm{2}}\:\mathrm{cos}\:{x} \\ $$$$\left({ii}\right)\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}+{x}\right)\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right)=−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{cos}\:\frac{\pi}{\mathrm{2}}−\mathrm{cos}\:\mathrm{2}{x}\right)=\frac{\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2}} \\…
Question Number 92781 by i jagooll last updated on 09/May/20 $$\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:=\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} +\mathrm{1}}\right)\: \\ $$ Commented by john santu last updated on 09/May/20 $$\mathrm{tan}\:\left(\mathrm{tan}^{−\mathrm{1}}…
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Question Number 92691 by john santu last updated on 08/May/20 $$\mathrm{find}\:{x}\:{in}\:{eq}\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right) \\ $$ Commented by Prithwish Sen 1 last updated on 08/May/20 $$\mathrm{let}\:\mathrm{tan}^{−\mathrm{1}}…
Question Number 158173 by France last updated on 31/Oct/21 $$\mathrm{simplify}\:\mathrm{the}\:\mathrm{expression}\:\left(\mathrm{1}+\mathrm{sin}\:\boldsymbol{\phi}\right)/\left(\mathrm{5}+\mathrm{3tan}\:\boldsymbol{\phi}−\mathrm{4cos}\:\boldsymbol{\phi}\right)\:\mathrm{using}\:\mathrm{small}\:\mathrm{angles}\:\mathrm{approximation}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{containing}\:\phi^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 27104 by ktomboy1992 last updated on 02/Jan/18 $$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}\:\:\:\mathrm{sin}\:\mathrm{60}°=?} \\ $$ Commented by mrW1 last updated on 02/Jan/18 $${what}\:{do}\:{you}\:{mean}? \\ $$$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}}…
Question Number 92585 by john santu last updated on 08/May/20 $$\mathrm{sin}\:\mathrm{2z}\:+\:\mathrm{5}\left(\mathrm{sin}\:\mathrm{z}+\mathrm{cos}\:\mathrm{z}\right)+\mathrm{1}=\mathrm{0} \\ $$ Commented by john santu last updated on 08/May/20 $$\mathrm{1}+\mathrm{sin}\:\mathrm{2z}=\left(\mathrm{sin}\:\mathrm{z}+\mathrm{cos}\:\mathrm{z}\right)^{\mathrm{2}} \\ $$$$\Rightarrow\left(\mathrm{sin}\:\mathrm{z}+\mathrm{cos}\:\mathrm{z}\right)\left(\mathrm{sin}\:\mathrm{z}+\mathrm{cos}\:\mathrm{z}+\mathrm{5}\right)=\mathrm{0} \\…
Question Number 26981 by Tinkutara last updated on 31/Dec/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{y}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equations} \\ $$$${x}\mathrm{sin}^{\mathrm{3}} {y}\:+\:\mathrm{3}{x}\mathrm{sin}\:{y}\:\mathrm{cos}^{\mathrm{2}} {y}\:=\:\mathrm{63}\:\mathrm{and}\:{x}\mathrm{cos}^{\mathrm{3}} {y} \\ $$$$+\:\mathrm{3}{x}\mathrm{cos}{y}\:\mathrm{sin}^{\mathrm{2}} {y}\:=\:\mathrm{62}\:\mathrm{simultaneously}. \\ $$$$\mathrm{Then}\:\mathrm{tan}\:{y}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by ajfour…
Question Number 26951 by Tinkutara last updated on 31/Dec/17 Answered by prakash jain last updated on 31/Dec/17 $$\mathrm{5cos}\:\mathrm{2}\theta+\mathrm{12sin}\:\mathrm{2}\theta=\mathrm{13} \\ $$$$\mathrm{5}\left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \theta\right)+\mathrm{24sin}\:\theta\mathrm{cos}\:\theta=\mathrm{13} \\ $$$$\mathrm{10sin}^{\mathrm{2}} \theta−\mathrm{24sin}\:\theta\mathrm{cos}\:\theta+\mathrm{8}=\mathrm{0} \\…
Question Number 92461 by jagoll last updated on 07/May/20 $$\mathrm{cos}\:\left(\frac{\mathrm{3x}}{\mathrm{4}}−\pi\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{2x}\right) \\ $$$$\mathrm{x}\:\in\:\left[\mathrm{0},\:\pi\:\right]\: \\ $$ Commented by john santu last updated on 07/May/20 $$−\mathrm{cos}\left(\frac{\mathrm{3x}}{\mathrm{4}}\right)\:=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{2x}\right)\: \\ $$$$\mathrm{cos}\:\left(\frac{\mathrm{3x}}{\mathrm{4}}\right)\:=\:\mathrm{sin}\:\left(\mathrm{2x}−\frac{\pi}{\mathrm{4}}\right)…