Category: Trigonometry

Question Number 192763 by TUN last updated on 26/May/23 $$Provethat:$$$$sinA+sinB+sinC>2$$$$(A,B,C\in \frac{\pi }{2})$$ Answered by JDamian last updated on 26/May/23 $${really}? \…

Question Number 192733 by Mingma last updated on 25/May/23 Answered by MM42 last updated on 25/May/23 $$\frac{1-\frac{2tanA}{1+{tan}^{2}A}}{1+\frac{1-{tan}^{2}A}{1+{tan}^{2}A}}=tanA-1$$$$\frac{{tan}^{2}A-2tanA+1}{2}=tanA-1$$$${tan}^{\mathrm{2}}…

Question Number 127081 by slahadjb last updated on 26/Dec/20 $$Solvein\mathbb{C}$$$${\left(\frac{1+iz}{1-iz}\right)}^n=e_{}^{i{\theta }_n}$$$${\theta }_n\in \mathbb{R}$$$$n\in \mathbb{N}$$ Answered by Dwaipayan…

Question Number 127045 by benjo_mathlover last updated on 26/Dec/20 $$\frac{\cos 1°+\cos 2°+\cos 3°+\dots +\cos 44°}{\sin 1°+\sin 2°+\sin 3°+\dots +\sin 44°}=?$$ Answered by liberty last updated on 26/Dec/20 $$\frac{\cos (22.5°-21.5°)+\cos (22.5°-20.5°)+\dots +\cos (22.5°+20.5°)+\cos (22.5°+21.5°)}{\sin (22.5°-21.5°)+\sin (22.5°-20.5°)+\dots +\sin (22.5°+20.5°)+\sin (22.5+21.5°)}=$$$$\frac{2\cos 22.5°\cos 21.5°+2\cos 22.5°\cos 20.5°+\dots +2\cos 22.5°\cos 0.5°}{2\sin 22.5°\cos 21.5°+2\sin 22.5°\cos 20.5°+\dots +2\sin 22.5°\cos 0.5°}=$$$$\frac{\mathrm{cos}\:\mathrm{22}.\mathrm{5}°\left(\mathrm{cos}\:\mathrm{21}.\mathrm{5}°+\mathrm{cos}\:\mathrm{20}.\mathrm{5}°+…+\mathrm{cos}\:\mathrm{0}.\mathrm{5}°\right)}{\mathrm{sin}\:\mathrm{22}.\mathrm{5}°\left(\mathrm{cos}\:\mathrm{21}.\mathrm{5}°+\mathrm{cos}\:\mathrm{20}.\mathrm{5}°+…+\mathrm{cos}\:\mathrm{0}.\mathrm{5}°\right)}\:= \…

Question Number 192537 by cortano12 last updated on 20/May/23 $$\{\begin{array}{l}\tan (\alpha +2\beta )=\sqrt{1+2\mathrm{k}}\\ \tan {}^2(\alpha +\beta )\{1+\mathrm{k}\tan {}^2\beta \}=\mathrm{k}+\tan {}^2\beta \end{array}$$$$\mathrm{Find}\cot 2\beta .$$ Answered by a.lgnaoui last updated on 20/May/23 $$\:\:\:\:\mathrm{tan}\:\left[\left(\alpha+\beta\right)+\beta\right]=\sqrt{\mathrm{1}+\mathrm{2k}}\:\:\:\:\:\:\:\:\:\:\:…