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
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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
1.证明:sin^4α－cos^4α
=(sin^2α－cos^2α)*(sin^2α+cos^2α)
=(sin^2α－cos^2α)*1
=sin^2α－cos^2α
2.证明:sin^4α+sin^2αcos^2α+cos^2α
=(sin^2a)^2+sin^2αcos^2α+cos^2α
=sin^2a*(sin^2a+cos^2a)+cos^2a
=sin^2a*1+cos^2a
=1

sin^4α－cos^4α
=(sin^2α－cos^2α)*(sin^2α+cos^2α)
=sin^2α－cos^2α
sin^4α+sin^2αcos^2α+cos^2α
=(sin^2a)^2+sin^2αcos^2α+cos^2α
=sin^2a*(sin^2a+cos^2a)+cos^2a
=sin^2a*1+cos^2a
=1

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