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Alistratov
@Alistratov
July 2022
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sin^6(pi/8)+cos^6(9pi/8)
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sedinalana
Verified answer
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
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Answers & Comments
Verified answer
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