Category: Trigonometry

Question Number 116281 by aye48 last updated on 02/Oct/20 $$\mathrm{Prove}\mathrm{that}\sin 10°\sin 30°\sin 50°\sin 70°.$$ Answered by Dwaipayan Shikari last updated on 02/Oct/20 $$\sin \theta \sin 3\theta \sin 5\theta \sin 7\theta \theta =10°$$$$\frac{1}{2}\left(2\sin \theta \sin 7\theta \right)\frac{1}{2}\left(2\sin 5\theta \sin 3\theta \right)$$$$\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{cos6}\theta−\mathrm{cos8}\theta\right)\left(\mathrm{cos2}\theta−\mathrm{cos8}\theta\right)…

Question Number 181719 by cortano1 last updated on 29/Nov/22 Answered by mr W last updated on 29/Nov/22 $$sayBA=a$$$${BD}^2=4^2+8^2-2\times 4\times 8\cos 120°$$$${BD}^{\mathrm{2}}…

Question Number 181592 by mathlove last updated on 27/Nov/22 $$provethat$$$$\frac{1}{cos0cos1}+\frac{1}{cos1cos2}+\dots \dots +\frac{1}{cos88cos89}=\frac{cos1}{{sin}^{2}1}$$ Answered by som(math1967) last updated on 27/Nov/22 $$\frac{1}{sin1}[\frac{sin(1-0)}{cos0cos1}+\frac{sin(2-1)}{cos1cos2}+$$$$\left….+\frac{{sin}\left(\mathrm{89}−\mathrm{88}\right)}{{cos}\mathrm{88}{cos}\mathrm{89}}\right]…

Question Number 50397 by Abdo msup. last updated on 16/Dec/18 $$calculateartan\left(2\right)+arctan\left(5\right)+arctan\left(8\right)$$ Answered by mr W last updated on 17/Dec/18 $${x}=\mathrm{tan}^{−\mathrm{1}} \mathrm{2}+\mathrm{tan}^{−\mathrm{1}} \mathrm{8} \…

Question Number 115798 by aye48 last updated on 28/Sep/20 Commented by bemath last updated on 29/Sep/20 $$\sin \alpha .\cos \beta =\frac{9}{10}$$$$\Rightarrow 2\sin \alpha .\cos \beta =\frac{9}{5}$$$$\Rightarrow \sin (\alpha +\beta )+\sin (\alpha -\beta )=\frac{9}{5}$$$$\Rightarrow \sin (\alpha +\beta )=\frac{9}{5}-\frac{4}{5}=1$$…