Question

请问他怎么化简成标准形式呢？

Answer 1

f = 2cos²x - sin(2x-7π/6)
= 1 + cos2x - sin2xcos7π/6 + cos2xsin7π/6
= 1 + cos2x + (√3/2)sin2x + (1/2)cos2x
= (√3/2)sin2x + (3/2)cos2x + 1
= √3(sin2xcosπ/3+cos2xsinπ/3) +1
= √3sin(2x+π/3) + 1

追问

sin7π/6=-1/2吧？

对吗？

sin7π/6=-1/2吗？

追答

是的

追问

那您应该是有一步算错了吧

追答

嗯！
f(x) = 2cos²x - sin(2x-7π/6)
= 1 + cos2x - sin2xcos7π/6 + cos2xsin7π/6
= 1 + cos2x + (√3/2)sin2x - (1/2)cos2x
= (√3/2)sin2x + (1/2)cos2x + 1
= (sin2xcosπ/6+cos2xsinπ/6) +1
= sin(2x+π/6) + 1

追问

嘻嘻，辛苦！