Category: Trigonometry

Question Number 171596 by nadovic last updated on 18/Jun/22 $$Showthat\frac{\cos 70°-\cos 20°}{\sin 70°-\sin 20°}=-1$$ Commented by mr W last updated on 18/Jun/22 $$\cos 70°=\cos (90°-20°)=\sin 20°$$$$\cos 20°=\cos (90°-70°)=\sin 70°$$$$\frac{\mathrm{cos}\:\mathrm{70}°−\mathrm{cos}\:\mathrm{20}°}{\mathrm{sin}\:\mathrm{70}°−\mathrm{sin}\:\mathrm{20}°}\:…

Question Number 171574 by cortano1 last updated on 18/Jun/22 Answered by mr W last updated on 18/Jun/22 Commented by mr W last updated on 18/Jun/22…

Question Number 105916 by bobhans last updated on 02/Aug/20 $$provethat\cot x.\cot 2x+\cot 2x.\cot 3x+2=$$$$\cot x.(\cot x-\cot 3x)$$ Answered by bemath last updated on 01/Aug/20 $$\cot x\cot 2x+\cot 2x\cot 3x=$$$$\mathrm{cot}\:\mathrm{2}{x}\:\left(\mathrm{cot}\:{x}+\mathrm{cot}\:\mathrm{3}{x}\right)= \…

Question Number 171389 by cortano1 last updated on 14/Jun/22 $$\tan {}^2\left(\frac{\pi }{7}\right)+\tan {}^2\left(\frac{3\pi }{7}\right)+\tan {}^2\left(\frac{5\pi }{7}\right)=?$$ Commented by Shrinava last updated on 14/Jun/22 $$\mathrm{Or}\:\mathrm{sec}^{\mathrm{2}} \:\frac{\pi}{\mathrm{7}}\:+\:\mathrm{sec}^{\mathrm{2}} \:\frac{\mathrm{3}\pi}{\mathrm{7}}\:+\:\mathrm{sec}^{\mathrm{2}}…

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…