（1）根号2cos3x+根号6sin3x； （2）cos5π/12-根号3sin5π/12

三倍角公式
sin3α=4sinα·sin(π/3+α)sin(π/3-α)
cos3α=4cosα·cos(π/3+α)cos(π/3-α)
根号2cos3x+根号6sin3x=根号2(cos3x+根号3sin3x)=2根号2(sin3x+π/6)
估计难求具体值,试一下
根号2cos3x+根号6sin3x=4根号2sinx·sin(π/3+x)sin(π/3-x)+4根号6cosx·cos(π/3+x)cos(π/3-x)
=4根号2sinx·(3/4cosx^2-1/4sinx^2)+4根号6cosx·(1/4cosx^2-3/4sinx^2)
=根号2sinx·(3cosx^2-sinx^2)+根号6cosx·(cosx^2-3sinx^2)
=3根号2sinxcosx^2-根号2sinx^3+根号6cosx^3-3根号6cosxsinx^2
看这样子,这肯定是化简题,不可能得到一个常数来
cos5π/12-根号3sin5π/12
=2cos(π/3+5π/12)
=2cos3π/4
=-根号2