Question Number 85372 by john santu last updated on 21/Mar/20
$$\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{4cos}\:^{\mathrm{2}} {x}\:=\:\mathrm{3}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x} \\ $$$${find}\:\mathrm{tan}\:{x}.\: \\ $$
Answered by john santu last updated on 21/Mar/20
$$\mathrm{tan}\:^{\mathrm{2}} {x}\:−\:\mathrm{4}\:=\:\mathrm{3}\:\mathrm{tan}\:{x} \\ $$$$\mathrm{tan}\:^{\mathrm{2}} {x}\:−\:\mathrm{3tan}\:{x}\:−\:\mathrm{4}\:=\:\mathrm{0} \\ $$$$\mathrm{tan}\:{x}\:=\:\frac{\mathrm{3}\:\pm\:\mathrm{5}}{\mathrm{2}}\:\Rightarrow\:\begin{cases}{\mathrm{tan}\:{x}\:=\:\mathrm{4}}\\{\mathrm{tan}\:{x}\:=\:−\mathrm{1}}\end{cases} \\ $$