化简cos(π/4-α)²+cos(π/4+α)²
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注意诱导公式O(∩_∩)O~；cos(π/4-α)²+cos(π/4+α)²=cos(π/4-α)²+sin【π/2-(π/4+α)】²=cos(π/4-α)²+sin（π/4-α)²=1
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cos(π/4-α)²+cos(π/4+α)²
=[1+cos(π/2-2α)]/2+[1+cos(π/2+2α)]/2
=(1+sin2α)/2+(1-sin2α)/2
=1/2+1/2*sin2α+1/2-1/2*sin2α
=1
cos(π/4-α)²+cos(π/4+α)²
=cos(π/4-α)²+cos(π/2-π/4+α)²
=cos(π/4-α)²+cos[π/2-(π/4-α)]²
=cos(π/4-α)²+sin(π/4-α)²
=1
=[1+cos(π/2-2α)]/2+[1+cos(π/2+2α)]/2
=(1+sin2α)/2+(1-sin2α)/2
=1/2+1/2*sin2α+1/2-1/2*sin2α
=1
cos(π/4-α)²+cos(π/4+α)²
=cos(π/4-α)²+cos(π/2-π/4+α)²
=cos(π/4-α)²+cos[π/2-(π/4-α)]²
=cos(π/4-α)²+sin(π/4-α)²
=1
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