Category: Trigonometry

Question Number 105764 by bobhans last updated on 31/Jul/20 $$\left(1\right)If\cos (\alpha +\beta )=\frac{4}{5}and\sin (\alpha -\beta )=\frac{5}{13}$$$$where0<\alpha <\frac{\pi }{4}.Find\tan 2\alpha .$$$$\left(2\right)\cos {}^4\left(\frac{\pi }{8}\right)+\cos {}^4\left(\frac{3\pi }{8}\right)+\cos {}^4\left(\frac{5\pi }{8}\right)+\cos {}^4\left(\frac{7\pi }{8}\right)?$$ Commented by Dwaipayan Shikari last…

Question Number 105766 by bramlex last updated on 31/Jul/20 $$Ifp=\sin \left(\frac{\pi }{18}\right)\sin \left(\frac{5\pi }{18}\right)\sin \left(\frac{7\pi }{18}\right)$$$$findthevalueofp.$$ Answered by som(math1967) last updated on 31/Jul/20 $$\mathrm{let}\frac{\pi }{18}=\alpha$$$$\therefore\mathrm{p}=\mathrm{sin}\alpha\mathrm{sin5}\alpha\mathrm{sin7}\alpha \…

Question Number 105692 by bramlex last updated on 31/Jul/20 $$\cos {}^2\left(5x\right)+\sin {}^2\left(7x\right)=1$$ Answered by john santu last updated on 31/Jul/20 $$\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{5}{x}\right)+\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{7}{x}\right)=\mathrm{1}…

Question Number 105619 by bobhans last updated on 30/Jul/20 $$find\mathcal{G}eneralsolution\cot x+\cot 2x+\cot 3x=0$$$$$$ Answered by bemath last updated on 30/Jul/20 $$\Leftrightarrow\mathrm{cot}\:\left({x}\right)+\frac{\mathrm{cot}\:^{\mathrm{2}} \left({x}\right)−\mathrm{1}}{\mathrm{2cot}\:\left({x}\right)}+\frac{\mathrm{3cot}\:\left({x}\right)−\mathrm{cot}\:^{\mathrm{3}} \left({x}\right)}{\mathrm{1}−\mathrm{3cot}\:^{\mathrm{2}} \left({x}\right)}=\:\mathrm{0}…

Question Number 170968 by 281981 last updated on 05/Jun/22 Commented by mr W last updated on 05/Jun/22 $${\tan }^2(x+y)+{\cos }^2(x+y)-1+{(y+1)}^2=0$$$$\mathrm{tan}^{\mathrm{2}} \:\left({x}+{y}\right)−\mathrm{sin}^{\mathrm{2}} \:\left({x}+{y}\right)+\left({y}+\mathrm{1}\right)^{\mathrm{2}}…