sin^4 22.5°-cos^4 22.5°=

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sin^4 22.5°-cos^4 22.5°=
sin^4 22.5°-cos^4 22.5°=

sin^4 22.5°-cos^4 22.5°=
sin^4 22.5°-cos^4 22.5°
=(sin²22.5°+cos²22.5°)(sin²22.5°-cos²22.5°)
=sin²22.5°-cos²22.5° (因为sin²22.5°+cos²22.5=1)
=-(cos²22.5°-sin²22.5°)
=-cos45°
=-√2/2

原式=(sin²22.5+cos²22.5)(sin²22.5-cos²22.5)
=1*(-cos45)
=-√2/2

解sin^4 22.5°-cos^4 22.5°
=(sin^2 22.5°-cos^2 22.5°)(sin^2 22.5°+cos^2 22.5°)
=(sin^2 22.5°-cos^2 22.5°)
=-(cos^2 22.5°-sin^2 22.5°)
=-cos45°
=-√2/2

sin^4 22.5°-cos^4 22.5° 平方差
=(sin²22.5°+cos²22.5°)(sin²22.5°-cos²22.5°)
=sin²22.5°-cos²22.5°
=-(cos²22.5°-sin²22.5°) 两倍角公式
=-cos(2×22.5°)
=-cos45°
=-√2/2
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