Упростить: cos^3(pi/12) + sin^3(pi/12)

Question

Упростить:
cos^3(pi/12) + sin^3(pi/12)

Answer 1

Cos^3(pi/12) + sin^3(pi/12)=
(cos(pi/12) + sin(pi/12)) (cos^2(pi/12) -cos(pi/12) sin(pi/12) +sin^2(pi/12))=
=(cos(pi/12) + sin(pi/12)) (1-1/2sin(pi/6)=(√((cos(pi/12) + sin(pi/12))^2) 3/4=
=3/4[√(1+2cos(pi/12) sin(pi/12)]=3/4 [√(1+ sin(pi/6))]=3/4[√(1+1/2)]=3/4[√(3/2)]