Question

(cos П/12 - sin П/12)*(cos^3 П/12 + sin^3 П/12)

Answer 1

$(cosfrac{pi}{12}-sinfrac{pi}{12})(cos^3frac{pi}{12}+sin^3frac{pi}{12})=(cosfrac{pi}{12}-sinfrac{pi}{12})(cosfrac{pi}{12}+sinfrac{pi}{12})cdot\ \ cdot(cos^2frac{pi}{12}-cosfrac{pi}{12}sinfrac{pi}{12}+sin^2frac{pi}{12})=(cos^2frac{pi}{12}-sin^2frac{pi}{12})(1-0.5sin(2cdotfrac{pi}{12}))=\ \ =cos(2cdotfrac{pi}{12})(1-0.5sin(2cdotfrac{pi}{12}))=cosfrac{pi}{6}(1-0.5sinfrac{pi}{6})=frac{sqrt{3}}{2}(1-0.5cdot0.5)=frac{3sqrt{3}}{8}$