Question

若sinα＋cosα＝√2，则sin^4－cos^4等于？

写出过程……谢谢各位大大了

Answer 1

sinα＋cosα＝√2
两边平方
1+sin2a=2
sin2a=1

sin^4－cos^4
=（sin^2－cos^2）（sin^2+cos^2）
=sin^2－cos^2
=-2cos2a
=0

Answer 2

sinα＋cosα＝√2
两边平方得
sin²α+2sinacosa+cos²a=2
∴sinαcosα=1/2

(sinα-cosα)²=1-2sinacosa=0
∴sina-cosa=0

∴sin^4α-cos^4α
=(sin²α+cos²α)(sinα+cosα)(sina-cosa)
=0

Answer 3

sinx+cosx=√2.两边平方
(sinx+cosx)^2=2
(sinx)^2+(cosx)^2+2sinxcosx=2
1+sin2x=2.
sin2x=1
cos2x=0
sin^4α-cos^4α
=(sin^2α-cos^2α)(sin^2α+cos^2α)
=sin^2α-cos^2α
=(sinα-cosα)(sinx+cosx)
=0*√2
=0

Answer 4

sinα＋cosα＝√2
(sinα+cosα)²=2
2sinαcosα=1
1-2sinαcosα=0
(sinα-cosα)²=0
sinα-cosα=0

sin^4α－cos^4α
=(sin²α+cos²α)(sin²α-cos²α)
=(sin²α+cos²α)(sinα+cosα)(sinα-cosα)
=0