Question

化简cos方(π/4-α)+cos方(π/4+α)

化简cos方(π/4-α)+cos方(π/4+α)

Answer 1

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