已知sin^4x+cos^4x=1,求sinx+cosx的值
人气:370 ℃ 时间:2020-02-03 22:13:04
解答
sin⁴x+cos⁴x=1
(sin²x+cos²x)²-2sin²xcos²x=1
1-2sin²xcos²x=1
2sin²xcos²x=0
sinxcosx=0
(sinx+cosx)²=sin²x+2sinxcosx+cos²x=1+0=1
sinx+cosx=1或sinx+cosx=-1
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