α,β是锐角,且α+β=2π/3,求cos^α+cos^β的取值范围._数学解答

α,β是锐角,且α+β=2π/3,求cos^α+cos^β的取值范围.

人气：360 ℃　时间：2020-06-13 16:39:19

解答

cos^2α+cos^2β
=(1+cos2α)/2+(1+cos2β)/2
=1+1/2*(cos2α+cos2β)
=1+1/2*2*cos(α+β)*cos(α-β)
=1-1/2*cos(α-β)
α,β是锐角,且α+β=2π/3,
所以
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