Category: Trigonometry

Question Number 148381 by liberty last updated on 27/Jul/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 82767 by jagoll last updated on 24/Feb/20 $$\mathrm{If}\frac{\sin (\mathrm{A}+\theta )}{\sin (B+\theta )}=\sqrt{\frac{\sin 2A}{\sin 2B}}$$$$provethat\tan {}^2\theta =\tan A.\tan B$$ Commented by jagoll last updated on 24/Feb/20 $$thankyoumrwandjohn$$…

Question Number 17153 by Tinkutara last updated on 01/Jul/17 $$\mathrm{If}m,n\in N(n>m),\mathrm{then}\mathrm{number}\mathrm{of}$$$$\mathrm{solutions}\mathrm{of}\mathrm{the}\mathrm{equation}$$$$n\mid \sin x\mid =m\mid \sin x\mid \mathrm{in}[0,2\pi ]\mathrm{is}$$ Answered by mrW1 last updated on 01/Jul/17 $${n}\mid\mathrm{sin}\:{x}\mid\:=\:{m}\mid\mathrm{sin}\:{x}\mid \…

Question Number 17150 by Tinkutara last updated on 01/Jul/17 $$\mathrm{If}\mathrm{the}\mathrm{equation}\cos x+3\cos \left(2Kx\right)=4$$$$\mathrm{has}\mathrm{exactly}\mathrm{one}\mathrm{solution},\mathrm{then}$$$$\left(1\right)K\mathrm{is}\mathrm{a}\mathrm{rational}\mathrm{number}\mathrm{of}\mathrm{the}\mathrm{form}$$$$\frac{P}{P+1},P\ne -1$$$$\left(2\right)K\mathrm{is}\mathrm{irrational}\mathrm{number}\mathrm{whose}$$$$\mathrm{rational}\mathrm{approximation}\mathrm{does}\mathrm{not}$$$$\mathrm{exceed}2$$$$\left(\mathrm{3}\right)\:{K}\:\mathrm{is}\:\mathrm{irrational}\:\mathrm{number} \…

Question Number 17148 by Tinkutara last updated on 01/Jul/17 $$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{solutions}\mathrm{of}\mathrm{the}\mathrm{equation}$$$$\cos \left(\pi \sqrt{x-4}\right)\cos \left(\pi \sqrt{x}\right)=1\mathrm{is}$$ Answered by ajfour last updated on 01/Jul/17 $$\Rightarrow \cos \left(\pi \sqrt{\mathrm{x}-4}\right)=\pm 1$$$$\mathrm{and}\:\:\:\mathrm{cos}\:\left(\pi\sqrt{\mathrm{x}}\right)=\pm\mathrm{1} \…