若sin^4a+cos^4a=1,则sina+cosa=
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 20:12:05
![若sin^4a+cos^4a=1,则sina+cosa=](/uploads/image/z/746191-55-1.jpg?t=%E8%8B%A5sin%5E4a%2Bcos%5E4a%3D1%2C%E5%88%99sina%2Bcosa%3D)
若sin^4a+cos^4a=1,则sina+cosa=
若sin^4a+cos^4a=1,则sina+cosa=
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