Category: Trigonometry

Question Number 133587 by bemath last updated on 23/Feb/21 $$\mathrm{Find}\mathrm{the}\mathrm{exact}\mathrm{value}\mathrm{of}\cos 12°.$$ Answered by Dwaipayan Shikari last updated on 23/Feb/21 $$sin\frac{\pi }{60}=sin\frac{\pi }{10}cos\frac{\pi }{12}-sin\frac{\pi }{12}cos\frac{\pi }{10}$$$$=\frac{\sqrt{5}-1}{4}.\frac{\sqrt{2+\sqrt{3}}}{2}-\frac{\sqrt{10-2\sqrt{5}}}{4}.\frac{\sqrt{2+\sqrt{3}}}{2}$$$$=\frac{\mathrm{1}}{\mathrm{16}}\left(\left(\sqrt{\mathrm{5}}−\mathrm{1}\right)\left(\sqrt{\mathrm{6}}−\sqrt{\mathrm{2}}\right)−\left(\sqrt{\mathrm{6}}+\sqrt{\mathrm{2}}\right)\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}\right)…

Question Number 68021 by anaplak last updated on 03/Sep/19 Commented by Tanmay chaudhury last updated on 03/Sep/19 Answered by Tanmay chaudhury last updated on 03/Sep/19…

Question Number 133443 by mnjuly1970 last updated on 22/Feb/21 $$\dots \dots nicecalculus\dots \dots .$$$$ifa,b,c⩾0$$$$and::{acos}^2\left(x\right)+{bsin}^2\left(x\right)⩽c$$$$thenprovethat::$$$$\sqrt{a}{cos}^2\left(x\right)+\sqrt{b}{sin}^2\left(x\right)⩽\sqrt{c}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…………. \…

Question Number 133347 by rs4089 last updated on 21/Feb/21 $$foratriangleABC\dots$$$$findminimumvalueof$$$$CosA.CosB.CosC$$ Commented by mr W last updated on 21/Feb/21 $${i}\:{think}\:{there}\:{is}\:{no}\:{minimum},…

Question Number 67495 by TawaTawa last updated on 28/Aug/19 Commented by Prithwish sen last updated on 28/Aug/19 $$\sin (\frac{5}{2}\pi +\mathrm{x})=\mathrm{Cos}(\mathrm{x}+\frac{1}{2}-\frac{1}{9})\Rightarrow \mathrm{Cosx}=\mathrm{Cos}(\mathrm{x}+\frac{7}{18})$$$$\mathrm{x}=2\mathrm{n}\pi \pm (\mathrm{x}+\frac{7}{18})\mathrm{n}\in \mathbb{Z}$$ Commented by TawaTawa…