利用和差角公式化简(2)sin(π/3+α)+sin(π/3-α)(2)sin(π/3+α)+sin(π/3-α)(3)cos(π/4+α)-cos(π/4-α)(4)cos(60°+α)+cos(60°-α)(5)sin(α-β)cosβ+cos(α-β)sinβ(6)cos(α+β)cosβ+sin(α+β)sinβ

Answer 1

（2）原式=[sin(π/3)cosα+cos(π/3)sinα]+[sin(π/3)cosα-cos(π/3)sinα]
=2sin(π/3)cosα
=2(√3/2)cosα
=√3cosα.
（3）原式=[cos(π/4)cosα-sin(π/4)sinα]-[cos(π/4)cosα+sin(π/4)sinα]
=-2sin(π/4)sinα
=-2(√2/2)sinα
=-√2sinα.
（4）原式=[cos(60°)cosα-sin(60°)sinα]+[cos(60°)cosα+sin(60°)sinα]
=2cos(60°)cosα
=2(1/2)cosα
=cosα.
（5）原式=sin[(α-β)+β]=sinα.
（6）原式=cos[(α+β)-β]=cosα.