Question

Помогите решить пример :3

Answer 1

√2/2-(cosπ/8+sinπ/8)²=√2/2-(cos²π/8+2cosπ/8·sinπ/8+sin²π/8)=
=√2/2-(1+sinπ/4)=√2/2-(1+√2/2)=√2/2-(2+√2)/2=(√2-2-√2)/2=-2/2=-1

Answer 2

$frac{ sqrt{2}}{2}-(cos^{2}(frac{ pi }{8})+2*cos(frac{ pi }{8})*sin(frac{ pi }{8})+sin^{2}(frac{ pi }{8}))=frac{ sqrt{2}}{2}-(1+2*cos(frac{ pi }{8})*sin(frac{ pi }{8}))=frac{ sqrt{2}}{2}-1-sin(frac{2pi }{8})=frac{ sqrt{2}}{2}-1-sin(frac{pi }{4})=frac{ sqrt{2}}{2}-1-frac{ sqrt{2}}{2}=-1$