Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 106295 by bobhans last updated on 04/Aug/20

$$\frac{1}{\cos \mathrm{x}}+\frac{\sqrt{3}}{\sin \mathrm{x}}=4$$

Answered by bemath last updated on 04/Aug/20

$$\sin \mathrm{x}+\sqrt{3}\cos \mathrm{x}=4\sin \mathrm{xcos}\mathrm{x}$$$$\frac{1}{2}\sin \mathrm{x}+\frac{\sqrt{3}}{2}\cos \mathrm{x}=\sin 2\mathrm{x}$$$$\sin 30°\sin \mathrm{x}+\cos 30°\cos \mathrm{x}=\sin 2\mathrm{x}$$$$\cos (30°-\mathrm{x})=\sin 2\mathrm{x}=\cos (90°-2\mathrm{x})$$$$\{\begin{array}{l}30°-\mathrm{x}=90°-2\mathrm{x}+\mathrm{k}.360°\\ 30°-\mathrm{x}=-90°+2\mathrm{x}+\mathrm{k}.360°\end{array}$$$$\{\begin{array}{l}\mathrm{x}=60°+\mathrm{k}.360°\\ \mathrm{x}=40°+\mathrm{k}.120°\end{array}$$

Answered by Dwaipayan Shikari last updated on 04/Aug/20

$$sinx+\sqrt{3}cosx=4sinxcosx$$$$\frac{1}{2}sinx+\frac{\sqrt{3}}{2}cosx=sin2x$$$$sin(x+\frac{\pi }{3})=sin2x$$$$2x=2\pi k\pm (x+\frac{\pi }{3})$$$$x=2\pi k+\frac{\pi }{3}=(6k+1)\frac{\pi }{3}(k\in \mathbb{Z})$$$$3x=2\pi k-\frac{\pi }{3}$$$$x=(6k-1)\frac{\pi }{9}$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com