Question Number 20648 by Joel577 last updated on 30/Aug/17
$$\mathrm{If}\:\:\frac{{F}}{\mathrm{sin}\:\left({A}\:−\:{a}\right)}\:=\:\frac{{W}}{\mathrm{sin}\:{A}},\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{tan}\:{A}\:=\:\frac{{W}\:\mathrm{sin}\:{a}}{{W}\:\mathrm{cos}\:{a}\:−\:{F}} \\ $$
Answered by $@ty@m last updated on 30/Aug/17
$${Given}, \\ $$$$\:\frac{{F}}{\mathrm{sin}\:\left({A}\:−\:{a}\right)}\:=\:\frac{{W}}{\mathrm{sin}\:{A}} \\ $$$$\Rightarrow{FsinA}={Wsin}\left({A}−{a}\right) \\ $$$$\Rightarrow{FsinA}={WsinAcosa}−{WcosAsina} \\ $$$$\Rightarrow{FtanA}={WtanAcosa}−{WsinA} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left({dividing}\:{the}\:{eqn}.\:{by}\:{cosA}\right) \\ $$$$\Rightarrow{WsinA}={tanA}\left({Wcosa}−{F}\right) \\ $$
Commented by Joel577 last updated on 31/Aug/17
$${thank}\:{you}\:{very}\:{much} \\ $$