Category: Trigonometry

Question Number 12572 by tawa last updated on 25/Apr/17 $$\mathrm{prove}\mathrm{that}\mathrm{if},$$$$\sin \left(\theta \right)=\frac{1-\mathrm{x}}{1+\mathrm{x}}\mathrm{then}\tan (\frac{\mathrm{x}}{4}-\frac{\theta }{2})=\sqrt{\mathrm{x}}$$ Commented by mrW1 last updated on 26/Apr/17 $$Ithinkyoumean\mathrm{t}a\mathrm{n}(\frac{\pi }{4}-\frac{\theta }{2})=\sqrt{\mathrm{x}}$$ Answered…

Question Number 12525 by tawa last updated on 24/Apr/17 $$\mathrm{Use}\mathrm{the}\mathrm{substitution}\mathrm{t}=\sin \left(\theta \right)\mathrm{to}\mathrm{solve}\mathrm{the}\mathrm{equation}$$$${2\sin }^4\left(\theta \right)-{9\sin }^3\left(\theta \right)+{14\sin }^2\left(\theta \right)-9\sin \left(\theta \right)+2=0,$$$$\mathrm{for}\mathrm{possible}\mathrm{values}\mathrm{of}\theta \mathrm{in}\mathrm{the}\mathrm{range}0⩽\theta ⩽2\pi$$ Answered by mrW1 last updated on…

Question Number 143499 by mnjuly1970 last updated on 15/Jun/21 Commented by MJS_new last updated on 15/Jun/21 $$$$$$\tan (60°-\alpha )=\frac{\sqrt{3}-\tan \alpha }{1+\sqrt{3}\tan \alpha }$$$$\tan (60°+\alpha )=\frac{\sqrt{3}+\tan \alpha }{1-\sqrt{3}\tan \alpha }$$$$\mathrm{tan}\:\mathrm{3}\alpha\:=\frac{\left(\mathrm{3}−\mathrm{tan}^{\mathrm{2}} \:\alpha\right)\mathrm{tan}\:\alpha}{\mathrm{1}−\mathrm{3tan}^{\mathrm{2}} \:\alpha}…

Question Number 143450 by bramlexs22 last updated on 14/Jun/21 $$whenx+y=\frac{2\pi }{3};x⩾0;y⩾0$$$$themaximumandtheminimum$$$$of\sin x+\sin yis\mathrm{\_}\mathrm{\_}\mathrm{\_}$$ Answered by EDWIN88 last updated on 16/Jun/21 $$\:\mathrm{y}=\:\frac{\mathrm{2}\pi}{\mathrm{3}}−\mathrm{x}\:\Rightarrow\mathrm{sin}\:\mathrm{y}=\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}−\mathrm{x}\right) \…

Question Number 143439 by ERA last updated on 14/Jun/21 $$\mathrm{sinx}+\sin 2\mathrm{x}+\sin 3\mathrm{x}+\dots ..+\mathrm{sinkx}=\sin \frac{\mathrm{kx}}{2}\times \frac{\sin \frac{\mathrm{k}+1}{2}\mathrm{x}}{\sin \frac{\mathrm{x}}{2}}$$$$\mathrm{prove}$$ Answered by Mathspace last updated on 14/Jun/21 $$A_n=sinx+sin\left(2x\right)+\dots +sin\left(nx\right)\Rightarrow$$$${A}_{{n}}…