cos(π⼀3-2x)怎样化等于sin(2x+π⼀6)

解: cos(π/3-2x)=cos(π/3)
sin(2x+π/6))=sin(π/6)
因为cos(π/3)=sin(π/6)
所以cos(π/3-2x)=sin(2x+π/6)

另一种解法:
cos(π/3-2x) 根据公式 cosx=sin(π/2-x) 得
=sin[π/2-(π/3-2x)]
=sin[（π/2-π/3）+2x]
=sin(2x+π/6)

希望对你有帮助

cos(π/3-2x)
=sin[π/2-(π/3-2x)]
=sin[（π/2-π/3）+2x]
=sin(2x+π/6)
一个角的余弦值等于它的余角的正弦值
或者说
两角互余，一个角的余弦值等于另一个角的正弦值

注：3^(1/2)为根号3
cos^2(π/12)为cos的平方π/121、f(x)=sinπ/3-cosπ/2
2cos^2(π/12)=sinπ/3-cosπ/2
2cos^2(π/3-π/4)=3^(1/2)-0
1
3^(1/2)=1
3^(1/2)
2、先化简：f(x)=sin2xcosπ/6
cos2xsinπ/6-cos2xcosπ/3
sin2xsinπ/3
1
cos2x=二分之根号三sin2x
1/2cos2x-1/2cos2x
二分之根号三sin2x
1
cos2x=根号三sin2x
cos2x
1=2sin(2x
π/6)
1
当sin(2x
π/6)等于1时取得最大值3
当
sin(2x
π/6)=1
等价于2x
π/6=2kπ
π/2
解得x=kπ
π/6
我写了这么多
怎么也得采纳吧
呵呵

解：
cos(π/3-2x)
=cos[2π-(π/3-2x)]
=cos(2x+5π/3)
=cos[π+(2x+2π/3)]
=-cos(2x+2π/3)
=-cos(π/2+2x+π/6)
=sin(2x+π/6)

cos(π/3-2x)=cos[(π/2-(2x+π/6)]=sin(2x+π/6)