Question Number 207498 by hardmath last updated on 17/May/24
$$\mathrm{cos2}\boldsymbol{\mathrm{x}}\:+\:\mathrm{sin}\boldsymbol{\mathrm{x}}\:=\:\mathrm{tg}\left(\mathrm{225}°\right)\centerdot\left(\mathrm{0},\mathrm{360}°\right) \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{roots}\:=\:? \\ $$
Answered by MM42 last updated on 17/May/24
$$−\mathrm{2}{sin}^{\mathrm{2}} {x}+{sinx}=\mathrm{0} \\ $$$${sinx}=\mathrm{0}\Rightarrow{x}=\pi \\ $$$${sinx}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}=\frac{\pi}{\mathrm{2}} \\ $$$$\Rightarrow{s}=\frac{\mathrm{3}\pi}{\mathrm{2}}\:\checkmark \\ $$$$ \\ $$
Commented by hardmath last updated on 17/May/24
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{professor} \\ $$