Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 103983 by I want to learn more last updated on 18/Jul/20

If α and β are two unequal angle, which satisfy the equation, a cos(α) + b sin(β) = c, show that (i) sin(((α + β)/2)) sec(((α − β)/2)) = (b/c) (ii) tan((α/2)) tan((β/2)) = ((c − a)/(c + a))

$$\mathrm{If}\:\:\alpha\:\:\mathrm{and}\:\:\beta\:\:\mathrm{are}\:\mathrm{two}\:\mathrm{unequal}\:\mathrm{angle},\:\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}, \\ $$$$\:\:\:\:\mathrm{a}\:\mathrm{cos}\left(\alpha\right)\:\:+\:\:\mathrm{b}\:\mathrm{sin}\left(\beta\right)\:\:=\:\:\mathrm{c},\:\:\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\:\:\:\mathrm{sin}\left(\frac{\alpha\:\:+\:\beta}{\mathrm{2}}\right)\:\mathrm{sec}\left(\frac{\alpha\:\:−\:\:\beta}{\mathrm{2}}\right)\:\:=\:\:\frac{\mathrm{b}}{\mathrm{c}} \\ $$$$\left(\mathrm{ii}\right)\:\:\:\:\:\mathrm{tan}\left(\frac{\alpha}{\mathrm{2}}\right)\:\mathrm{tan}\left(\frac{\beta}{\mathrm{2}}\right)\:\:=\:\:\frac{\mathrm{c}\:\:−\:\:\mathrm{a}}{\mathrm{c}\:\:+\:\:\mathrm{a}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com