Category: Trigonometry

Question Number 189026 by Rupesh123 last updated on 10/Mar/23 Answered by Ar Brandon last updated on 10/Mar/23 $${\cot }^{2}x+1={\mathrm{cosec}}^{2}x$$$$\mid 4-a\mid +1=\frac{\mid a\mid }{3},0<a⩽4$$$$\Rightarrow\mathrm{4}−{a}+\mathrm{1}=\frac{{a}}{\mathrm{3}}\:\Rightarrow{a}=\frac{\mathrm{15}}{\mathrm{4}} \…

Question Number 57915 by Tinkutara last updated on 14/Apr/19 Answered by mr W last updated on 14/Apr/19 $$(1-{\tan }^2\theta )(1+{\tan }^2\theta )+2^{{\tan }^2\theta }=0$$$${let}\:{t}=\mathrm{tan}^{\mathrm{2}} \:\theta\geqslant\mathrm{0}…

Question Number 57664 by necx1 last updated on 09/Apr/19 $$AluminouspointPisinsideacircle.$$$$ArayemanatesfromPandaftertwo$$$$reflectionsbythecircle,returnstoP.$$$$If\theta betheangleofincidence,a=the$$$$distanceofPfromthecentreofthe$$$$circleandb=thedistanceofthecentre$$$$fromthepointwheretherayinits$$$${course}\:{crosses}\:{its}\:{diameter}\:{through}\:{P}. \…

Question Number 188721 by Rupesh123 last updated on 06/Mar/23 Answered by Frix last updated on 06/Mar/23 $$x⩾0$$$$\Rightarrow$$$$0⩽\sqrt{x}<\mathrm{\infty }$$$$-2.73581\dots ⩽\sin x+2\sin 2x⩽2.73581\dots$$$$\:\:\:\:\:\:\:\:\:\:\left[\mathrm{Exact}\:\mathrm{values}\:\pm\frac{\left.\sqrt{\mathrm{6}\left(\mathrm{789}+\mathrm{43}\sqrt{\mathrm{129}}\right.}\right)}{\mathrm{32}}\right]…

Question Number 188645 by Rupesh123 last updated on 04/Mar/23 Answered by witcher3 last updated on 05/Mar/23 $$\mathrm{let}\mathrm{a}=\cos \left(\frac{\pi }{7}\right),\mathrm{b}=-\cos \left(\frac{2\pi }{7}\right);\mathrm{c}=\cos \left(\frac{3\pi }{7}\right)$$$$\mathrm{we}\:\mathrm{want}\:\mathrm{1}+\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} +\mathrm{a}^{\mathrm{3}} \mathrm{b}^{\mathrm{3}} +\mathrm{a}^{\mathrm{3}} \mathrm{c}^{\mathrm{3}}…