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Category: Trigonometry

Question-115798

Question Number 115798 by aye48 last updated on 28/Sep/20 Commented by bemath last updated on 29/Sep/20 $$\mathrm{sin}\:\alpha.\mathrm{cos}\:\beta\:=\:\frac{\mathrm{9}}{\mathrm{10}} \\ $$$$\Rightarrow\mathrm{2sin}\:\alpha.\mathrm{cos}\:\beta\:=\:\frac{\mathrm{9}}{\mathrm{5}} \\ $$$$\Rightarrow\mathrm{sin}\:\left(\alpha+\beta\right)+\mathrm{sin}\:\left(\alpha−\beta\right)\:=\:\frac{\mathrm{9}}{\mathrm{5}} \\ $$$$\Rightarrow\:\mathrm{sin}\:\left(\alpha+\beta\right)\:=\:\frac{\mathrm{9}}{\mathrm{5}}\:−\:\frac{\mathrm{4}}{\mathrm{5}}\:=\:\mathrm{1} \\ $$…

cos-pi-65-cos-2pi-65-cos-4pi-65-cos-8pi-65-cos-16pi-65-cos-32pi-65-

Question Number 115455 by bemath last updated on 26/Sep/20 $$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{8}\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{16}\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{32}\pi}{\mathrm{65}}\right)=? \\ $$ Commented by Adel last updated on 13/Jan/21 $$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{8}\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{16}\pi}{\mathrm{65}}\right).\mathrm{cos}\:\left(\frac{\mathrm{32}\pi}{\mathrm{65}}\right)=? \\ $$ Answered by TANMAY…

If-x-0-pi-2-and-2cos-x-sin-x-cos-x-tan-2-x-lt-sec-2-x-has-solution-set-is-a-lt-x-lt-b-find-the-value-of-a-b-

Question Number 115348 by bemath last updated on 25/Sep/20 $${If}\:{x}\:\in\:\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\right)\:{and}\:\mathrm{2cos}\:{x}\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)+\mathrm{tan}\:^{\mathrm{2}} {x}\:<\:\mathrm{sec}\:^{\mathrm{2}} {x}\: \\ $$$${has}\:{solution}\:{set}\:{is}\:{a}<{x}<{b}.\:{find}\:{the} \\ $$$${value}\:{of}\:{a}+{b} \\ $$ Answered by bobhans last updated on 25/Sep/20…

sec-sec-sin-2-2-3-sin-1-has-the-roots-are-1-and-2-Find-the-value-of-tan-1-tan-2-

Question Number 115345 by bemath last updated on 25/Sep/20 $$\mathrm{sec}\:\theta\:\left(\mathrm{sec}\:\theta\:\left(\mathrm{sin}\:^{\mathrm{2}} \theta\right)+\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\theta\right)=\mathrm{1} \\ $$$${has}\:{the}\:{roots}\:{are}\:\theta_{\mathrm{1}} \:{and}\:\theta_{\mathrm{2}} .\:{Find}\:{the} \\ $$$${value}\:{of}\:\mathrm{tan}\:\theta_{\mathrm{1}} ×\mathrm{tan}\:\theta_{\mathrm{2}} . \\ $$ Answered by bobhans last…

Minimum-value-of-function-f-x-16x-2-cos-2-x-4-x-cos-x-where-pi-lt-x-lt-0-

Question Number 115332 by bobhans last updated on 25/Sep/20 $${Minimum}\:{value}\:{of}\:{function}\: \\ $$$${f}\left({x}\right)=\:\frac{\mathrm{16}{x}^{\mathrm{2}} \:\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{4}}{{x}\:\mathrm{cos}\:{x}}\:{where}\:−\pi<{x}<\mathrm{0} \\ $$ Commented by bemath last updated on 25/Sep/20 $$\Leftrightarrow\:{f}\left({x}\right)=\mathrm{16}{x}\:\mathrm{cos}\:{x}\:+\:\mathrm{4}{x}^{−\mathrm{1}} \:\mathrm{sec}\:{x}…

If-sin-1-sin-2-sin-3-sin-44-cos-1-cos-2-cos-3-cos-44-then-4-4-3-4-2-4-

Question Number 115328 by bobhans last updated on 25/Sep/20 $${If}\:\frac{\mathrm{sin}\:\mathrm{1}°+\mathrm{sin}\:\mathrm{2}°+\mathrm{sin}\:\mathrm{3}°+…+\mathrm{sin}\:\mathrm{44}°}{\mathrm{cos}\:\mathrm{1}°+\mathrm{cos}\:\mathrm{2}°+\mathrm{cos}\:\mathrm{3}°+…+\mathrm{cos}\:\mathrm{44}°}=\chi \\ $$$${then}\:\chi^{\mathrm{4}} +\mathrm{4}\chi^{\mathrm{3}} +\mathrm{4}\chi^{\mathrm{2}} +\mathrm{4}= \\ $$ Answered by bemath last updated on 25/Sep/20 $$\:\:\mathrm{sin}\:\mathrm{44}°+\mathrm{sin}\:\mathrm{1}°=\mathrm{2sin}\:\left(\frac{\mathrm{45}°}{\mathrm{2}}\right).\mathrm{cos}\:\left(\frac{\mathrm{43}°}{\mathrm{2}}\right)…

If-2sin-3cos-3-2sin-2-3cos-2-

Question Number 180826 by mnjuly1970 last updated on 17/Nov/22 $$ \\ $$$$\:\:\:\:\mathrm{I}{f}\:\:,\:\:\:\mathrm{2}{sin}\left(\theta\:\right)−\mathrm{3}{cos}\left(\theta\right)\:=\mathrm{3} \\ $$$$\:\Rightarrow\:\:\:\mathrm{2}{sin}\left(\frac{\theta}{\mathrm{2}}\right)\:−\:\mathrm{3}{cos}\left(\frac{\theta}{\mathrm{2}}\right)\:=\:? \\ $$$$ \\ $$ Answered by mr W last updated on…