Category: Trigonometry

Question Number 219279 by Mingma last updated on 22/Apr/25 Answered by som(math1967) last updated on 22/Apr/25 $$\frac{2sin\frac{\beta +\alpha }{2}cos\frac{\alpha -\beta }{2}}{2\sin \frac{\alpha +\beta }{2}sin\frac{\alpha -\beta }{2}}=\sqrt{3}$$$$\Rightarrow cot\frac{\alpha -\beta }{2}=cot\frac{\pi }{6}$$$$\Rightarrow \alpha -\beta =\frac{\pi }{3}$$$$\sin 3\alpha +\sin \beta$$$$=\mathrm{2sin}\:\frac{\mathrm{3}\left(\alpha+\beta\right)}{\mathrm{2}}×\mathrm{cos}\:\frac{\mathrm{3}\left(\alpha−\beta\right)}{\mathrm{2}}…

Question Number 217783 by malwan last updated on 21/Mar/25 $$$$ Commented by malwan last updated on 21/Mar/25 $$$$ Commented by malwan…

Question Number 217146 by a.lgnaoui last updated on 02/Mar/25 $$\mathrm{determiner}\mathrm{le}\mathrm{cote}\mathrm{du}\mathrm{care}\mathbf{ABCD}$$$$\mathrm{inscrit}\mathrm{dans}\mathrm{l}\mathrm{elipse}\{(-3,+3):(-8,+8)\}$$ Commented by a.lgnaoui last updated on 02/Mar/25 Answered by mr W…

Question Number 216592 by Davidtim last updated on 11/Feb/25 $$ifwehavethefollowingsystem:$$$$\frac{tanx}{tany}=a$$$$x\pm y=\alpha$$$$wehavethegeneralcandition:$$$$-1⩽\left(\frac{a-1}{a+1}\right)sin\alpha ⩽1$$$$ifyouapplythegeneralcanditionby$$$$thefollowingsystemitdoesnotgive$$$${us}\:{the}\:{reality},\:{despite}\:{this}\:{system}\:{have} \…

Question Number 216454 by a.lgnaoui last updated on 08/Feb/25 $$\mathrm{Reponse}\mathrm{a}\mathrm{l}\mathrm{exercice}\mathrm{N}8:$$$$\mathrm{Reponses}\mathrm{par}\mathrm{ordre}:(1,2,3,4,5,6)$$$$\mathbf{imsge}1$$$$\mathbf{imsge}2$$$$\mathbf{image}3$$$$\mathbf{imsge}5$$$$\mathbf{imsge}4$$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{6} \…