Category: Trigonometry

Question Number 165070 by mathlove last updated on 25/Jan/22 Answered by bobhans last updated on 25/Jan/22 $$\cos \mathrm{x}-\sin \mathrm{x}=\sqrt{1-2\sin \mathrm{x}\cos \mathrm{x}}$$$$\Rightarrow \frac{\sqrt{1-2\sin \mathrm{x}\cos \mathrm{x}}}{\sin \mathrm{x}\cos \mathrm{x}}=2\sqrt{2}$$$$\sqrt{1-2\mathrm{t}}=2\sqrt{2}\mathrm{t},[\mathrm{t}=\sin \mathrm{x}\cos \mathrm{x}]$$$$\Rightarrow 1-2\mathrm{t}={8\mathrm{t}}^2$$$$\Rightarrow\mathrm{8t}^{\mathrm{2}}…

Question Number 33941 by manishprajapati076@gmail.com last updated on 28/Apr/18 $$9$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 99385 by Ar Brandon last updated on 20/Jun/20 $$\mathrm{Prove}{\sin }^4\mathrm{A}=\frac{3}{8}-\frac{1}{2}\cos 2\mathrm{A}+\frac{1}{8}\cos 4\mathrm{A}$$ Answered by Ar Brandon last updated on 20/Jun/20 $$\begin{vmatrix}{\mathrm{z}^{\mathrm{n}} −\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{n}} }=\mathrm{2}{i}\mathrm{sin}\left(\mathrm{nA}\right)\:\:,\:\:\mathrm{z}^{\mathrm{n}}…

Question Number 164901 by cortano1 last updated on 23/Jan/22 Answered by bobhans last updated on 23/Jan/22 $$\Rightarrow \frac{\sin {}^4\mathrm{x}}{\cos {}^4\mathrm{x}}-\frac{2-3\cos {}^2\mathrm{x}}{\cos {}^2\mathrm{x}}=0$$$$\Rightarrow\:\frac{\left(\mathrm{1}−\mathrm{c}\right)^{\mathrm{2}} }{\mathrm{c}^{\mathrm{2}} }\:−\frac{\mathrm{2}−\mathrm{3c}}{\mathrm{c}}\:=\:\mathrm{0}\:,\:\mathrm{c}\:=\:\mathrm{cos}\:^{\mathrm{2}}…

Question Number 164820 by Avijit007 last updated on 22/Jan/22 Answered by Ar Brandon last updated on 22/Jan/22 $$\mathrm{Let}x\mathrm{and}y\mathrm{be}\mathrm{complex}\mathrm{numbers}\mathrm{such}\mathrm{that}x=e^{i\vartheta }\mathrm{and}y=e^{i\mathrm{\Phi }}$$$$\mathrm{Then}\:{x}^{{m}} +\frac{\mathrm{1}}{{x}^{{m}} }=\mathrm{2cos}\left({m}\vartheta\right)\:\mathrm{and}\:{y}^{{m}} +\frac{\mathrm{1}}{{y}^{{m}} }=\mathrm{2cos}\left({m}\Phi\right)…