Category: Trigonometry

Question Number 18069 by tawa tawa last updated on 14/Jul/17 $$\mathrm{ai})\mathrm{If}\theta \mathrm{is}\mathrm{the}\mathrm{angle}\mathrm{in}\mathrm{the}\mathrm{fourth}\mathrm{quadrant}\mathrm{satisfying}\mathrm{the}\mathrm{equation}:{\cot }^2\theta =4$$$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{function}:\mathrm{f}\left(\theta \right)=\frac{1}{\sqrt{5}}(\sec \theta -\mathrm{cosec}\theta )$$$$\mathrm{aii})\mathrm{Prove}\mathrm{that}:\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}=\mathrm{cosec}\theta +\cot \theta ,\mathrm{if}\cos \theta \ne 1$$$$\left(\mathrm{b}\right)\mathrm{Let}\mathrm{R}\mathrm{be}\mathrm{a}\mathrm{positive}\mathrm{real}\mathrm{number}\mathrm{and}\mathrm{let}\alpha \mathrm{satisfy}\mathrm{the}\mathrm{inequality}$$$$0<\alpha <360.\mathrm{express}\mathrm{the}\mathrm{function}2\sin \theta +\cos \theta \mathrm{in}\mathrm{the}\mathrm{form}\mathrm{Rsin}(\theta +\alpha ).$$$$\mathrm{Hence},\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\theta \mathrm{between}0\mathrm{and}360\mathrm{which}\mathrm{satisfy}\mathrm{the}\mathrm{equation}.$$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3cos}\theta\:+\:\mathrm{6sin}\theta\:=\:\mathrm{1} \…

Question Number 18063 by Tinkutara last updated on 14/Jul/17 $$\mathrm{The}\mathrm{angles}A,B,C\mathrm{of}\mathrm{a}\mathrm{triangle}ABC$$$$\mathrm{satisfy}4\cos A\cos B+\sin 2A+\sin 2B+$$$$\sin 2C=4.\mathrm{Then}\mathrm{which}\mathrm{of}\mathrm{the}\mathrm{following}$$$$\mathrm{statements}\mathrm{is}/\mathrm{are}\mathrm{correct}?$$$$\left(1\right)\mathrm{The}\mathrm{triangle}ABC\mathrm{is}\mathrm{right}\mathrm{angled}$$$$\left(2\right)\mathrm{The}\mathrm{triangle}ABC\mathrm{is}\mathrm{isosceles}$$$$\left(3\right)\mathrm{The}\mathrm{triangle}ABC\mathrm{is}\mathrm{neither}$$$$\mathrm{isosceles}\:\mathrm{nor}\:\mathrm{right}\:\mathrm{angled} \…

Question Number 83582 by jagoll last updated on 04/Mar/20 $$\mathrm{Given}\mathrm{A}={580}^{\mathrm{o}}$$$$\mathrm{find}\sin \left(\frac{\mathrm{A}}{2}\right)\mathrm{in}\mathrm{term}\sin \left(\mathrm{A}\right)$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 18003 by Tinkutara last updated on 13/Jul/17 $$\mathrm{The}\mathrm{value}\mathrm{of}\cos A\cdot \cos 2A\cdot {\cos 2}^{2}A\dots ..\cos \left(2^{n-1}A\right),$$$$\mathrm{where}A\in R\mathrm{may}\mathrm{be}$$$$\left(1\right)1$$$$\left(2\right)2$$$$\left(3\right)-1$$$$\left(\mathrm{4}\right)\:\frac{\mathrm{sin}\:\mathrm{2}^{{n}} \:{A}}{\mathrm{2}^{{n}} \:\mathrm{sin}\:{A}} \…

Question Number 83513 by jagoll last updated on 03/Mar/20 $$\mathrm{If}\mathrm{m}\tan (\theta -{30}^{\mathrm{o}})=\mathrm{n}\tan (\theta +{12}^{\mathrm{o}})$$$$\mathrm{prove}\mathrm{that}\cos 2\theta =\frac{\mathrm{m}+\mathrm{n}}{2(\mathrm{m}-\mathrm{n})}$$ Commented by mind is power last updated on 04/Mar/20…