Category: Trigonometry

Question Number 106387 by bemath last updated on 05/Aug/20 $$\cot \theta +\cot (\frac{\pi }{4}+\theta )=2$$$$\theta =?$$ Answered by 1549442205PVT last updated on 05/Aug/20 $$\cot \theta +\cot (\frac{\pi }{4}+\theta )=2$$$$\Leftrightarrow\frac{\mathrm{sin}\left(\mathrm{2}\theta+\frac{\pi}{\mathrm{4}}\right)}{\mathrm{sin}\theta\mathrm{sin}\left(\frac{\pi}{\mathrm{4}}+\theta\right)}=\mathrm{2}\Leftrightarrow\mathrm{sin}\left(\frac{\pi}{\mathrm{4}}+\mathrm{2}\theta\right)=\mathrm{2sin}\theta\mathrm{sin}\left(\frac{\pi}{\mathrm{4}}+\theta\right) \…

Question Number 171858 by Mikenice last updated on 21/Jun/22 $$solve:$$$$findthevalueofxandybetween{0}^{°}and{180}^{°}whichsatisfythesimultaneouseqn$$$$sin(x+y)=\frac{\sqrt{2}}{2}$$$$cos2x=-\frac{1}{2}$$ Terms of Service Privacy Policy…

Question Number 106286 by bemath last updated on 04/Aug/20 $$\mathrm{arc}\tan \left(\frac{\mathrm{x}+1}{\mathrm{x}-1}\right)+\mathrm{arc}\tan \left(\frac{\mathrm{x}-1}{\mathrm{x}}\right)=\mathrm{arc}\tan (-7)$$$$\mathrm{for}\mathrm{x}\mathrm{real}\mathrm{number}$$ Answered by bobhans last updated on 04/Aug/20 $$\to \mathrm{arc}\tan \left(\frac{\mathrm{x}+1}{\mathrm{x}-1}\right)+\mathrm{arc}\tan \left(\frac{\mathrm{x}-1}{\mathrm{x}}\right)=\mathrm{arc}\tan (-7)$$$$\mathrm{tan}\:\left(\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right)+\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}\right)\right)=\mathrm{tan}\:\left(\mathrm{arc}\:\mathrm{tan}\:\left(−\mathrm{7}\right)\right) \…

Question Number 106214 by john santu last updated on 03/Aug/20 $$\mathrm{solve}:\mathrm{arc}\cos (\mathrm{x}-1)=2\mathrm{arc}\cos \left(\mathrm{x}\right)$$$$\mathrm{where}\mathrm{x}\mathrm{is}\mathrm{real}.$$ Answered by bobhans last updated on 03/Aug/20 $$\Rightarrow \cos \left(\mathrm{arc}\cos (\mathrm{x}-1)\right)=\cos \left(2\mathrm{arc}\cos \left(\mathrm{x}\right)\right)$$$$\Rightarrow\:\mathrm{x}−\mathrm{1}\:=\:\mathrm{2}\:\mathrm{cos}\:^{\mathrm{2}}…

Question Number 171719 by cortano1 last updated on 20/Jun/22 $$\frac{1}{1+\sin {}^{2}x}+\frac{1}{1+\cos {}^{2}x}=\frac{48}{35}$$ Commented by infinityaction last updated on 20/Jun/22 $$\sin x=\pm \frac{1}{2},\pm \frac{\sqrt{3}}{2}$$ Commented…