Sin^6(pi/8)+cos^6(9pi/8)

Question

Sin^6(pi/8)+cos^6(9pi/8)

Answer 1

Sin^6(π/8)+cos^6(π+π/8)=sin^6(π/8)+cos^6π/8=
=(1-cosπ/4)³/8+(1+cosπ/4)³/8=1/8*((1-1/√2)³+(1+1/√2)³)=
=1/8*(1-3/√2+3/2-1/2√2+1+3/√2+3/2+1/2√2)=1/8*5=5/8