Question Number 157494 by MathSh last updated on 23/Oct/21
Answered by MJS_new last updated on 24/Oct/21
$$\mathrm{let}\:{s}=\mathrm{sin}\:{x} \\ $$$$\sqrt{−\mathrm{9}{s}^{\mathrm{2}} +\mathrm{12}{s}+\mathrm{13}}=−\frac{\mathrm{4}{s}^{\mathrm{2}} −\mathrm{32}{s}−\mathrm{13}}{\mathrm{8}} \\ $$$${s}^{\mathrm{4}} −\mathrm{16}{s}^{\mathrm{3}} +\frac{\mathrm{187}}{\mathrm{2}}{s}^{\mathrm{2}} +\mathrm{4}{s}−\frac{\mathrm{663}}{\mathrm{16}}=\mathrm{0} \\ $$$$\mathrm{no}\:``\mathrm{nice}''\:\mathrm{solution} \\ $$$${s}\approx−.\mathrm{649720963256}\vee{s}\approx.\mathrm{682719298518} \\ $$
Commented by MathSh last updated on 24/Oct/21
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{dear}\:\boldsymbol{\mathrm{S}}\mathrm{er}\:\mathrm{cool} \\ $$