化简cos方(π/4-α)+cos方(π/4+α)

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化简cos方(π/4-α)+cos方(π/4+α)
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化简cos方(π/4-α)+cos方(π/4+α)
化简cos方(π/4-α)+cos方(π/4+α)

化简cos方(π/4-α)+cos方(π/4+α)
原式=(COSπ/4COSα+SINπ/4SINα)²+(COSπ/4COSα-SINπ/4SINα)²
=(√2/2COSα+√2/2SINα)²+(√2/2COSα-√2/2SINα)²
=1/2(COS²α+2COSαSINα+SIN²α)+1/2(COS²α-2COSαSINα+SIN²α)
=1/2(2COS²α+2SIN²α)
=1/2×2
=1