Category: Trigonometry

Question Number 112542 by bobhans last updated on 08/Sep/20 $$\mathrm{If}7\sin \mathrm{y}=8\sin (\mathrm{y}+45°).\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\tan (\mathrm{y}+45°)?$$ Answered by bemath last updated on 08/Sep/20 $$\mathrm{let}\mathrm{x}=\mathrm{y}+45°;\mathrm{y}=\mathrm{x}-45°$$$$\iff 7\sin (\mathrm{x}-45°)=8\sin \mathrm{x}$$$$\Leftrightarrow\:\mathrm{7}\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}.\mathrm{sin}\:\mathrm{x}−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}.\mathrm{cos}\:\mathrm{x}\right)\:=\:\mathrm{8sin}\:\mathrm{x} \…

Question Number 112466 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by 1549442205PVT last updated on 08/Sep/20 $$\mid \mathrm{cosx}\mid ⩾1-{\sin }^2\mathrm{x}\iff \mid \mathrm{cosx}\mid ⩾{\cos }^2\mathrm{x}=\mid \mathrm{cosx}{\mid }^2$$$$\iff \mid \mathrm{cosx}\mid ⩽1.\mathrm{The}\mathrm{last}\mathrm{inequality}\mathrm{is}$$$$\mathrm{always}\:\mathrm{true}\:\forall\mathrm{x}.\mathrm{Hence},\mid\mathrm{cosx}\mid\geqslant\mathrm{1}−\mathrm{sin}^{\mathrm{2}}…

Question Number 177914 by mathlove last updated on 11/Oct/22 $$\left(1\right)\frac{2sin26+2cos64}{4sin13cos13}=?$$$$\left(2\right)\frac{1}{sec15sin15cos30}=?$$ Answered by Rasheed.Sindhi last updated on 11/Oct/22 $$\left(1\right)\frac{2sin26+2cos64}{4sin13cos13}=?$$$$\:\frac{\mathrm{2}{sin}\mathrm{26}+\mathrm{2}{cos}\mathrm{64}}{\mathrm{2}{sin}\mathrm{26}\:}−\mathrm{1}+\mathrm{1} \…

Question Number 177792 by cortano1 last updated on 09/Oct/22 $$\mathrm{Let}{\mathrm{f}}_{\mathrm{k}}\left(\mathrm{x}\right)=\frac{1}{\mathrm{k}}(\sin {}^{\mathrm{k}}\left(\mathrm{x}\right)+\cos {}^{\mathrm{k}}\left(\mathrm{x}\right))$$$$\mathrm{for}\mathrm{k}=1,2,3,\dots .$$$$\mathrm{Prove}\mathrm{that}$$$${\mathrm{f}}_4\left(\mathrm{x}\right)-{\mathrm{f}}_6\left(\mathrm{x}\right)=\frac{1}{12}\mathrm{for}\mathrm{all}\mathrm{real}\mathrm{numbers}\mathrm{x}$$ Answered by…

Question Number 112254 by john santu last updated on 07/Sep/20 $$\sin \left(\frac{\pi }{7}\right).\sin \left(\frac{2\pi }{7}\right).\sin \left(\frac{3\pi }{7}\right)=?$$ Answered by bemath last updated on 07/Sep/20 Terms of Service Privacy Policy…