根号2/4sin（π/4-x）+根号6/4cos（π/4-x） 化简

题目

根号2/4sin（π/4-x）+根号6/4cos（π/4-x） 化简
根号2/4就是四分之根号二

答案

√2/4 sin（π/4-x）+√6/4 cos（π/4-x）
=√2/2 [1/2 sin（π/4-x）+√3/2 cos（π/4-x）]
=√2/2 [cosπ/3 sin（π/4-x）+sinπ/3 cos（π/4-x）]
=√2/2 [ sin（π/4-x+π/3）]
=√2/2 [ sin（7π/12-x）]
=√2/2 [ sin（π/2+π/12-x）]
=√2/2 [ cos（π/12-x）]