求证sin^4α－cos^4α=sin^2α－cos^2α和sin^4α+sin^2αcos^2α+cos^2α=1

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求证sin^4α－cos^4α=sin^2α－cos^2α和sin^4α+sin^2αcos^2α+cos^2α=1
求证sin^4α－cos^4α=sin^2α－cos^2α和sin^4α+sin^2αcos^2α+cos^2α=1

求证sin^4α－cos^4α=sin^2α－cos^2α和sin^4α+sin^2αcos^2α+cos^2α=1
sin^4α－cos^4α=sin^2α－cos^2α
利用sin^2x +cos^2x=1
sin^4x - cos^4x = (sin^2x + cos^2x) (sin^2x + cos^2x)
=sin^2x + cos^2x
sin^4x + sin^2x cos^2x +cos^2x
=sin^x ( sin^2x +c0s^2x ) + cos ^2x
= sin^2x +c0s^2x
=1
两道题关键是：（1）公式sin^2x +cos^2x=1
（2）分解因式

1.左边=sin^4α－cos^4α=（sin^2α－cos^2α）（sin^2α+cos^2α）
=sin^2α－cos^2α=右边
2.左边=sin^4α+sin^2αcos^2α+cos^2α=（sin^2α+cos^2α）^2
=1=右边

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