神马作文网若sin^4a+cos^4a=1,则sina+cosa=
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若sin^4a+cos^4a=1,则sina+cosa=
(1) 当 sin a =0 时,
cos a = ±√ [ 1 -(sin a)^2 ]
= ±1,
满足 (sin a)^4 +(cos a)^4 =1.
此时 sin a +cos a = ±1.
(2) 当 sin a = ±1 时,
cos a = ±√ [ 1 -(sin a)^2 ]
=0.
满足 (sin a)^4 +(cos a)^4 =1.
此时 sin a +cos a = ±1.
(3) 当 sin a≠0 且 sin a ≠ ±1 时,
0< (sin a)^2
cos a = ±√ [ 1 -(sin a)^2 ]
= ±1,
满足 (sin a)^4 +(cos a)^4 =1.
此时 sin a +cos a = ±1.
(2) 当 sin a = ±1 时,
cos a = ±√ [ 1 -(sin a)^2 ]
=0.
满足 (sin a)^4 +(cos a)^4 =1.
此时 sin a +cos a = ±1.
(3) 当 sin a≠0 且 sin a ≠ ±1 时,
0< (sin a)^2
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