Category: Trigonometry

Question Number 104016 by Dwaipayan Shikari last updated on 18/Jul/20 Answered by OlafThorendsen last updated on 18/Jul/20 $$\arctan x-\arctan y=\arctan \frac{x-y}{1+xy}$$$$\arctan (2k+1)-\arctan (2k-1)=\arctan \frac{(2k+1)-(2k-1)}{1+(2k+1)(2k-1)}$$$$=\:\:\mathrm{arctan}\frac{\mathrm{2}}{\mathrm{4}{k}^{\mathrm{2}} }\:=\:\mathrm{arctan}\frac{\mathrm{1}}{\mathrm{2}{k}^{\mathrm{2}} } \…

Question Number 103984 by dw last updated on 18/Jul/20 $${\mathit{t}\mathit{a}\mathit{n}}^2\left(\mathit{x}\right)+{\mathit{t}\mathit{a}\mathit{n}}^2\left(2\mathit{x}\right)+{\mathit{t}\mathit{a}\mathit{n}}^2\left(4\mathit{x}\right)=33$$$$\mathit{x}=?$$ Commented by behi83417@gmail.com last updated on 19/Jul/20 $$\mathrm{Nice}\:\mathrm{to}\:\mathrm{see}\:\mathrm{you}\:\mathrm{again}\:\mathrm{mr}\:\mathrm{proph}:\mathrm{MJS}.…

Question Number 38288 by ajfour last updated on 23/Jun/18 $$\tan \alpha -\tan \beta =2\tan \theta$$$$a\sin \alpha -b\sin \beta =l\sin \theta$$$$express\sin \alpha ,\sin \beta intermsof\mathit{\theta }.$$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Jun/18 $${t}_{\mathrm{1}} ={tan}\frac{\alpha}{\mathrm{2}}\:\:\:{t}_{\mathrm{2}}…

Question Number 169295 by thfchristopher last updated on 28/Apr/22 $$\mathrm{Prove}\mathrm{without}\mathrm{using}\mathrm{Mathematical}$$$$\mathrm{Induction}\mathrm{that}:$$$${\cos }^{n}x=\frac{1}{2^{n-1}}\underset{k=0}{\sum ^{(n-1)/2}}{C}_k^n\cos (n-2k)x$$$$\mathrm{where}x\mathrm{is}\mathrm{any}\mathrm{real}\mathrm{number}\mathrm{and}n\mathrm{is}\mathrm{any}$$$$\mathrm{positive}\:\mathrm{odd}\:\mathrm{integer}. \…

Question Number 38151 by ajfour last updated on 22/Jun/18 $$a>b>0$$$$a^2\cos \theta -b^2\sin \theta =(a^2-b^2)\sin \theta \cos \theta$$$$Find\theta intermsofa,b.$$$$\theta \in (0,\frac{\pi }{2}).$$ Commented by behi83417@gmail.com…