Category: Trigonometry

Question Number 96766 by bemath last updated on 04/Jun/20 $$\mathrm{solve}:\tan x-\tan \left(2x\right)=2\sqrt{3}$$ Answered by bobhans last updated on 04/Jun/20 $$\Rightarrow \tan \left(x\right)-\frac{2\tan \left(x\right)}{1-\tan {}^2\left(x\right)}=2\sqrt{3}$$$$\mathrm{tan}\:\left({x}\right)−\mathrm{tan}\:^{\mathrm{3}} \left({x}\right)−\mathrm{2tan}\:\left({x}\right)=\:\mathrm{2}\sqrt{\mathrm{3}}\:−\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{tan}\:^{\mathrm{2}} \left({x}\right)…

Question Number 31030 by abdo imad last updated on 02/Mar/18 $$1)solveinRtheequation16u^5-20u^3+5u=0$$$$2)solveinRsin\left(5x\right)=0$$$$3)provethatsin\left(5x\right)=16{sin}^{5}x-20{sin}^{3}x+5sinxby$$$$usingmoivreformula.$$$$4)findthevaluesofsin\left(\frac{\pi }{5}\right)andsin\left(\frac{2\pi }{5}\right)$$$$\left.\mathrm{5}\right)\:{find}\:{cos}\left(\frac{\pi}{\mathrm{5}}\right)\:{and}\:{tan}\left(\frac{\pi}{\mathrm{5}}\right).…

Question Number 30929 by rahul 19 last updated on 28/Feb/18 $$\underset{n=0}{\sum ^{\mathrm{\infty }}}{\tan }^{-1}(n+\frac{1}{2})-{\tan }^{-1}(n-\frac{1}{2})=?$$ Commented by abdo imad last updated on 01/Mar/18…

Question Number 30856 by Joel578 last updated on 27/Feb/18 Commented by mrW2 last updated on 28/Feb/18 $$Questioniswrong.Itshouldbe:$$$${\sin }^{4}A=\dots$$ Answered by MJS…

Question Number 161907 by bobhans last updated on 24/Dec/21 $$\left(1\right)(\frac{1}{2}+\cos \frac{\pi }{20})(\frac{1}{2}+\cos \frac{3\pi }{20})(\frac{1}{2}+\cos \frac{9\pi }{20})(\frac{1}{2}+\cos \frac{27\pi }{20})=?$$$$\left(2\right)\tan \frac{\pi }{30}\tan \frac{7\pi }{30}\tan \frac{11\pi }{30}=?$$ Commented by blackmamba last updated on 24/Dec/21 $$\frac{\pi }{20}=9°;G=(\frac{1}{2}+\cos 9°)(\frac{1}{2}+\cos 27°)(\frac{1}{2}+\cos 81°)(\frac{1}{2}+\cos 243°)$$$$\:\left[\:$$\{\begin{array}{l}\cos 81°=\sin 9°\\ \cos 243°=-\sin 27°\end{array}$$\right] \…