Category: Trigonometry

Question Number 89351 by john santu last updated on 17/Apr/20 $$prove\tan 3^o\times \tan {39}^o\times \tan {89}^o=\tan {15}^o$$ Commented by MJS last updated on 17/Apr/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{wrong} \…

Question Number 23721 by Tinkutara last updated on 06/Nov/17 $$\mathrm{If}\mathrm{symbols}\mathrm{have}\mathrm{their}\mathrm{usual}\mathrm{meaning}$$$$\mathrm{then}\frac{1}{r^2}+\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}=$$$$\left(\mathrm{1}\right)\:\frac{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} }{{s}^{\mathrm{2}} }…

Question Number 154748 by imjagoll last updated on 21/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 21/Sep/21 $$\sin \left({3\log }_{\left(2\sin x\right)}\sqrt[3]{\pi }\right)=\frac{1}{2}\Rightarrow {\log }_{\left(2\sin x\right)}\pi =\frac{\pi }{6}$$$$\Rightarrow {\log }_{\pi }\left(2\sin x\right)=\frac{6}{\pi }\Rightarrow \sin x=\frac{1}{2}{\pi }^{\frac{6}{\pi }}$$$$\Rightarrow{x}=\mathrm{arcsin}\left(\frac{\mathrm{1}}{\mathrm{2}}\pi^{\frac{\mathrm{6}}{\pi}} \right)…

Question Number 89193 by jagoll last updated on 16/Apr/20 $$\cos x-\sin x=\frac{1}{2}$$$$\cos x\sin x=\frac{3}{8},\pi <x<2\pi$$$$\cos x+\sin x=?$$ Commented by Tony Lin last updated on 16/Apr/20 $$\because\pi<{x}<\mathrm{2}\pi…

Question Number 23648 by Tinkutara last updated on 03/Nov/17 $$\mathrm{If}\sin (3\theta +\alpha )+\sin (3\theta -\alpha )+\sin (\alpha -\theta )$$$$-\sin (\alpha +\theta )=\cos \alpha \mathrm{and}\cos \alpha \ne 0,\mathrm{then}$$$$\mathrm{which}\mathrm{of}\mathrm{the}\mathrm{values}\mathrm{of}\theta \mathrm{does}\mathrm{not}\mathrm{satisfy}$$$$\mathrm{the}\mathrm{given}\mathrm{equation}?$$$$\left(1\right)n\pi +{(-1)}^n\frac{\pi }{6},n\in I$$$$\left(2\right)n\pi +{(-1)}^n\frac{\pi }{10},n\in I$$$$\left(\mathrm{3}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{5}},\:{n}\:\in\:{I}…