Question Number 58853 by cesar.marval.larez@gmail.com last updated on 30/Apr/19
Answered by MJS last updated on 01/May/19
$$\frac{\frac{\mathrm{3}}{\mathrm{2}}\mathrm{sin}^{\mathrm{3}} \:\frac{\pi}{\mathrm{2}}\:+\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{3}}}{\mathrm{tan}\:\frac{\pi}{\mathrm{3}}\:+\mathrm{cos}\:−\mathrm{2}\pi}=\frac{\frac{\mathrm{3}}{\mathrm{2}}×\mathrm{1}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{2}}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}=−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$