Question Number 186830 by ajfour last updated on 11/Feb/23
Commented by ajfour last updated on 11/Feb/23
$${Find}\:{x}. \\ $$
Answered by ajfour last updated on 11/Feb/23
$$\frac{\mathrm{sin}\:\left(\phi−\theta\right)}{{x}^{\mathrm{2}} }=\frac{\mathrm{sin}\:\phi}{{x}^{\mathrm{3}} }=\frac{\mathrm{sin}\:\phi}{{x}+{c}} \\ $$$$\Rightarrow\:\:{x}=\frac{\mathrm{sin}\:\phi}{\mathrm{sin}\:\left(\phi−\theta\right)} \\ $$$${Also}\:\:\frac{\mathrm{sin}\:\phi}{{x}+{c}}==\frac{\mathrm{sin}\:\left(\phi−\theta\right)}{{x}^{\mathrm{2}} } \\ $$$$\Rightarrow\:\frac{\mathrm{sin}\:\phi}{\frac{\mathrm{sin}\:\phi}{\mathrm{sin}\:\left(\phi−\theta\right)}+{c}}=\frac{\mathrm{sin}\:^{\mathrm{3}} \left(\phi−\theta\right)}{\mathrm{sin}\:^{\mathrm{2}} \phi} \\ $$$$\Rightarrow \\ $$$$\mathrm{sin}\:^{\mathrm{3}} \phi=\mathrm{sin}\:^{\mathrm{2}} \left(\phi−\theta\right)\left\{\mathrm{sin}\:\phi+{c}\mathrm{sin}\:\left(\phi−\theta\right)\right\} \\ $$$$….. \\ $$