Category: Trigonometry

Question Number 170872 by mathlove last updated on 02/Jun/22 Answered by aleks041103 last updated on 04/Jun/22 $$\underset{k=1}{\prod ^{n-1}}sin\left(\frac{k\pi }{n}\right)=\underset{k=1}{\prod ^{n-1}}\frac{e^{\frac{k\pi i}{n}}-e^{-\frac{k\pi i}{n}}}{2i}=$$$$=\frac{\left(\underset{{k}=\mathrm{1}}…

Question Number 105285 by bemath last updated on 27/Jul/20 $$simplify\frac{\sin \theta }{1+\cot \theta }+\frac{\cos \theta }{1+\tan \theta }?$$ Commented by bemath last updated on 27/Jul/20 $$thankyou$$ Commented by som(math1967)…

Question Number 170752 by balirampatel last updated on 30/May/22 $$Solve:-\frac{sin\mathit{x}+cos\mathit{x}}{sin\mathit{x}-cos\mathit{x}}=\frac{\sqrt{3}-1}{\sqrt{3}+1}$$ Answered by Rasheed.Sindhi last updated on 30/May/22 $$\frac{sin\mathit{x}+cos\mathit{x}}{sin\mathit{x}-cos\mathit{x}}=\frac{\sqrt{3}-1}{\sqrt{3}+1}$$$$\overline{)\begin{array}{c}\frac{a}{b}=\frac{c}{d}\Rightarrow \frac{a+b}{a-b}=\frac{c+d}{c-d}\end{array}}$$$$\:\:\frac{\left({sin}\boldsymbol{{x}}\:+\:{cos}\boldsymbol{{x}}\right)+\left({sin}\boldsymbol{{x}}\:−\:{cos}\boldsymbol{{x}}\right)}{\left({sin}\boldsymbol{{x}}\:+\:{cos}\boldsymbol{{x}}\right)−\left({sin}\boldsymbol{{x}}\:−\:{cos}\boldsymbol{{x}}\right)} \…

Question Number 105112 by bemath last updated on 26/Jul/20 $$2\sqrt{3}\sin {}^2(x+\frac{3\pi }{2})+\sin 2x=0$$$$0⩽x⩽2\pi$$ Answered by john santu last updated on 28/Jul/20 $$\Leftrightarrow\:\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{cos}\:^{\mathrm{2}} \left({x}\right)+\:\mathrm{sin}\:\left(\mathrm{2}{x}\right)\:=\:\mathrm{0}…

Question Number 39486 by ajfour last updated on 06/Jul/18 $$\sin \theta =\sin \alpha \sin \left(\frac{\theta +\alpha }{2}\right)$$$$Express\theta explicitlyintermsof\alpha .$$ Commented by math khazana by abdo last updated on 07/Jul/18 $$\Rightarrow\mathrm{2}\:{sin}\left(\frac{\theta}{\mathrm{2}}\right){cos}\left(\frac{\theta}{\mathrm{2}}\right)={sin}\alpha\left({sin}\left(\frac{\theta}{\mathrm{2}}\right){cos}\left(\frac{\alpha}{\mathrm{2}}\right)+\right.…