作业帮若cos2x=√2/3,则cos^4x+sin^4x=多少?
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若cos2x=√2/3,则cos^4x+sin^4x=多少?
若cos2x=√2/3,则cos^4x+sin^4x=多少?
若cos2x=√2/3,则cos^4x+sin^4x=多少?
cos^4x+sin^4x
=[(1+cos²2x)/2]^2+[(1-cos²2x）/2]^2
然后带入cos2x=√2/3,
得到11/18
我算错了= =.决赛时候...粗心了..搞错符号了..
cos^4x+sin^4x-2cos²xsin²x+2cos²xsin²x
=(cos²x-sin²x)²+1/2sin²2x
=cos²2x+1/2（1-cos²2x)
=1/2cos²2x+1/2
=1/2*2/9+1/2
=1/9+1/2
=11/18
cos^4x+sin^4x=(sin²x+cos²x)²-2sinx²cos²x=1-(2sinxcosx)²/2
=1-(sin2x)²/2
(sin2x)²=1-(cos2x)²=1-2/9=7/9
原式=1-(7/9)/2=11/18
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