Category: Trigonometry

Question Number 140368 by meetbhavsar25 last updated on 06/May/21 Answered by benjo_mathlover last updated on 07/May/21 $${\cos }^{-1}\left(\frac{3+5\cos \mathrm{x}}{5+3\cos \mathrm{x}}\right)=\mathrm{u}$$$$\Rightarrow \frac{3+5\cos \mathrm{x}}{5+3\cos \mathrm{x}}=\cos \mathrm{u}$$$$\Rightarrow 3+5\cos \mathrm{x}=5\cos \mathrm{u}+3\cos \mathrm{u}\cos \mathrm{x}$$$$\Rightarrow\left(\mathrm{5}−\mathrm{3cos}\:\mathrm{u}\right)\mathrm{cos}\:\mathrm{x}\:=\:\mathrm{5cos}\:\mathrm{u}−\mathrm{3} \…

Question Number 9211 by tawakalitu last updated on 23/Nov/16 $$\mathrm{If}$$$$\mathrm{sinA}+\mathrm{sinB}=\mathrm{a}$$$$\mathrm{tanA}+\mathrm{tanB}=\mathrm{b}$$$$\mathrm{secA}+\mathrm{secB}=\mathrm{c}$$$$\mathrm{Prove}\mathrm{that},$$$$8\mathrm{bc}=\mathrm{a}{[{4\mathrm{b}}^2+({\mathrm{b}}^2-{\mathrm{c}}^2)]}^2$$…

Question Number 140177 by liberty last updated on 05/May/21 $$\mathrm{solution}\mathrm{set}\mathrm{equation}$$$$\sin {}^6\mathrm{x}+\cos {}^6\mathrm{x}=\frac{1}{4}\sin {}^{2}2\mathrm{x}$$ Answered by som(math1967) last updated on 05/May/21 $$\left({sin}^{\mathrm{2}}…

Question Number 140138 by henderson last updated on 04/May/21 Answered by mr W last updated on 04/May/21 Commented by mr W last updated on 04/May/21…

Question Number 74520 by chess1 last updated on 25/Nov/19 Answered by MJS last updated on 26/Nov/19 $$0⩽x<2\pi$$$$\tan x>\sin x$$$$\frac{\sin x}{\cos x}>\sin x$$$$\mathrm{case}1:\sin x>0\iff 0<x<\pi$$$$\frac{\mathrm{1}}{\mathrm{cos}\:{x}}>\mathrm{1}\:\Leftrightarrow\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}\vee\frac{\mathrm{3}\pi}{\mathrm{2}}<{x}<\mathrm{2}\pi…