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safin1ilya
@safin1ilya
July 2022
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cos^4 15pi/12-sin^4 5pi/12 Срочно)
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sedinalana
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Сos^4(5π/4)-sin^4(5π/12)=cos^4(π+π/4)-sin^4(π/2-π/12)=
=cos^4(π/4)-cos^4(π/12)=(1/√2)^4-(1+cos(π/6))²/4=
=1/4-(1+√3/2)²/4=1/4*(1-(1-√3/2)²)=1/4(1-1+√3-3/4)=
=1/4*(√3+3/4)=√3/4-3/16
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Verified answer
Сos^4(5π/4)-sin^4(5π/12)=cos^4(π+π/4)-sin^4(π/2-π/12)==cos^4(π/4)-cos^4(π/12)=(1/√2)^4-(1+cos(π/6))²/4=
=1/4-(1+√3/2)²/4=1/4*(1-(1-√3/2)²)=1/4(1-1+√3-3/4)=
=1/4*(√3+3/4)=√3/4-3/16