Question

f（x）＝2√3 sinxcosx＋2cos^2 x－1

请问f（x）＝2√3 sinxcosx＋2cos^2 x－1 怎么化简成Asin（w＋p）的形式？要详细过程哦！谢谢！！！

Answer 1

2sinxcosx=sin2x,2cos^2 x－1=cos2x
f（x）＝2√3 sinxcosx＋2cos^2 x－1
=√3sin2x+cos2x
=2(sin2x*√3/2+cos2x*1/2)
=2(sin2xcosπ/6+cos2xsinπ/6)
=2sin(2x+π/6)

Answer 2

2cos^2
这个^是表示平方么？
f（x）＝2√3 sinxcosx＋2cos^2 x－1
=√3sin2x+cos2x
=2(√3/2xsin2x+1/2xcos2x)
=2(cosπ/6xsin2+sinπ/6xcos2)
=2sin(2x+π/6)

注：2sinxcosx=sin2x
2cos^2 x－1=cos2x

Answer 3

f(x)=√3sin2x+cos2x
=2sin(2x+α)
tanα=1/√3
α=π/6
f(x)=2sin(2x+π/6)