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Category: Trigonometry

if-180-prove-sin-sin-sin-sin-pi-3-lt-4-sin-pi-3-

Question Number 116524 by abdullahquwatan last updated on 04/Oct/20 $$\mathrm{if}\:\alpha+\beta+\gamma=\mathrm{180}° \\ $$$$\mathrm{prove}: \\ $$$$\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta+\mathrm{sin}\:\gamma+\mathrm{sin}\:\frac{\pi}{\mathrm{3}}\:<\:\mathrm{4}\:\mathrm{sin}\:\frac{\pi}{\mathrm{3}} \\ $$ Commented by TANMAY PANACEA last updated on 04/Oct/20 $${solved}\:{but}\:{could}\:{not}\:{upload}\:{image}…

If-tan-and-tan-are-the-roots-of-equation-2x-2-5x-1-0-find-tan-2-2-tan-2-2-

Question Number 116503 by bemath last updated on 04/Oct/20 $$\mathrm{If}\:\mathrm{tan}\:\alpha\:\mathrm{and}\:\mathrm{tan}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{equation}\:\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{find}\:\begin{cases}{\mathrm{tan}\:\left(\frac{\alpha}{\mathrm{2}}+\mathrm{2}\beta\right)}\\{\mathrm{tan}\:\left(\mathrm{2}\alpha−\frac{\beta}{\mathrm{2}}\right)}\end{cases} \\ $$ Answered by bobhans last updated on 04/Oct/20 $$\Rightarrow\mathrm{x}_{\mathrm{1}}…

Given-sin-2-x-sin-x-1-find-the-value-of-cos-8-x-cos-6-x-cos-4-x-

Question Number 116493 by bemath last updated on 04/Oct/20 $$\mathrm{Given}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{1}\:,\:\mathrm{find}\: \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:^{\mathrm{8}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}\:=? \\ $$ Answered by bobhans last updated on 04/Oct/20…

If-8-cos-x-8-sin-x-3-what-is-the-value-of-55-tan-x-55-tan-x-

Question Number 116483 by bemath last updated on 04/Oct/20 $$\mathrm{If}\:\mathrm{8}\:\mathrm{cos}\:\mathrm{x}−\mathrm{8}\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{3}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{55}\:\mathrm{tan}\:\mathrm{x}\:+\:\frac{\mathrm{55}}{\mathrm{tan}\:\mathrm{x}}\:? \\ $$ Answered by mr W last updated on 04/Oct/20 $$\mathrm{8}\left(\mathrm{1}−\mathrm{tan}\:{x}\right)=\frac{\mathrm{3}}{\mathrm{cos}\:{x}} \\ $$$$\mathrm{64}\left(\mathrm{1}−\mathrm{tan}\:{x}\right)^{\mathrm{2}}…

If-sin-P-8-17-where-3pi-2-lt-P-lt-2pi-and-cos-Q-24-25-where-pi-lt-Q-lt-3pi-2-what-is-the-value-of-cos-2P-Q-

Question Number 116448 by bobhans last updated on 04/Oct/20 $$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{P}\right)\:=\:−\frac{\mathrm{8}}{\mathrm{17}}\:,\mathrm{where}\:\frac{\mathrm{3}\pi}{\mathrm{2}}<\mathrm{P}<\mathrm{2}\pi \\ $$$$\mathrm{and}\:\mathrm{cos}\:\left(\mathrm{Q}\right)=−\frac{\mathrm{24}}{\mathrm{25}},\:\mathrm{where}\:\pi<\mathrm{Q}<\frac{\mathrm{3}\pi}{\mathrm{2}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\left(\mathrm{2P}+\mathrm{Q}\right)\:=? \\ $$ Answered by bemath last updated on 04/Oct/20 $$\left(\mathrm{1}\right)\:\mathrm{cos}\:\left(\mathrm{P}\right)=\:\frac{\mathrm{15}}{\mathrm{17}}\:;\:\mathrm{sin}\:\left(\mathrm{Q}\right)=−\frac{\mathrm{7}}{\mathrm{25}} \\…

If-sin-45-x-1-3-where-45-lt-x-lt-90-What-is-the-value-of-6sin-x-2-2-

Question Number 116441 by bobhans last updated on 04/Oct/20 $$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{45}°−\mathrm{x}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{3}}\:,\:\mathrm{where}\:\mathrm{45}°<\mathrm{x}<\mathrm{90}° \\ $$$$.\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{6sin}\:\mathrm{x}−\sqrt{\mathrm{2}}\right)^{\mathrm{2}} \\ $$ Answered by bemath last updated on 04/Oct/20 $$\Rightarrow\mathrm{sin}\:\left(\mathrm{x}−\mathrm{45}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\:\mathrm{sin}\:\mathrm{x}−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\…

Determine-the-maximum-value-of-1-cos-x-sin-x-cos-x-2-where-x-ranges-over-all-real-numbers-

Question Number 116374 by bemath last updated on 03/Oct/20 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}+\mathrm{2}}\:\mathrm{where}\:\mathrm{x}\:\mathrm{ranges}\:\mathrm{over}\:\mathrm{all} \\ $$$$\mathrm{real}\:\mathrm{numbers}. \\ $$ Answered by MJS_new last updated on 03/Oct/20 $${x}=\mathrm{2arctan}\:{t} \\…

cos-56-cos-2-56-cos-2-2-56-cos-2-3-56-cos-2-23-56-

Question Number 181863 by greougoury555 last updated on 01/Dec/22 $$\:\mathrm{cos}\:\mathrm{56}°.\:\mathrm{cos}\:\left(\mathrm{2}.\mathrm{56}°\right).\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{2}} .\mathrm{56}°\right).\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{3}} .\mathrm{56}°\right)…\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{23}} .\mathrm{56}°\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com