Question Number 200788 by hardmath last updated on 23/Nov/23
$$\mathrm{sin}\boldsymbol{\mathrm{x}}\:\:\:+\:\:\:\mathrm{cos}\boldsymbol{\mathrm{x}}\:\:\:=\:\:\:\mathrm{tg}\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{x}\:=\:? \\ $$
Answered by Frix last updated on 23/Nov/23
$${x}=\mathrm{2tan}^{−\mathrm{1}} \:{t}\:\mathrm{leads}\:\mathrm{to} \\ $$$${t}^{\mathrm{4}} −\mathrm{4}{t}^{\mathrm{3}} −\mathrm{2}{t}^{\mathrm{2}} +\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{No}\:\mathrm{nice}\:\mathrm{solution}. \\ $$$${t}_{\mathrm{1}} \approx.\mathrm{513620} \\ $$$${t}_{\mathrm{2}} \approx\mathrm{4}.\mathrm{43911} \\ $$$${x}_{\mathrm{1}} \approx.\mathrm{948968}+\mathrm{2}{n}\pi \\ $$$${x}_{\mathrm{2}} =\mathrm{2}.\mathrm{69845}+\mathrm{2}{n}\pi \\ $$