sin^4a+cos^4a=1,则sina-cosa=
问题描述：
sin^4a+cos^4a=1,则sina-cosa=
答
sin^4a+cos^4a=1,
所以(sin^2a+cos^2a)^2=sin^4a+cos^4a+2sin^2a*cos^2a
1=1+2sin^2a*cos^2a
sinacosa=0
则(sina-cosa)^2=1-2sinacosa=1,
所以sina-cosa=±1
答
sin^4 a+cos^4 a=1
sin^4 a+2sin^2 a cos^2 a+cos^4 a=1+2sin^2 a cos^2 a
(sin^2 a+cos^2 a)^2=1+2sin^2 a cos^2 a
1=1+2sin^2 a cos^2 a
sin^2 a cos^2 a=0
sinacosa=0
sin^2 a-2sinacosa+cos^2 a = 1-2*0=1
(sina-cosa)^2=1
sina-cosa=正负1
答
sin^4a+cos^4a=(sin²a+cos²a)²-2sin²acos²a=1
1-2sin²acos²a=1
sin²acos²a=0
所以sina=0或cosa=0
sina=0,则cosa=±1
cosa=0,则sina=±1
所以 sina-cosa=1或-1