求证sin^4α－cos^4α=sin^2α－cos^2α和sin^4α+sin^2αcos^2α+cos^2α=1
问题描述：
求证sin^4α－cos^4α=sin^2α－cos^2α和sin^4α+sin^2αcos^2α+cos^2α=1
答
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
答
1.证明:sin^4α－cos^4α=(sin^2α－cos^2α)*(sin^2α+cos^2α)=(sin^2α－cos^2α)*1=sin^2α－cos^2α2.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=...