已知f(x)=根号3sinx+cosx,若f(a)=2/3,球cos(2a+π/3)的值

问题描述:

已知f(x)=根号3sinx+cosx,若f(a)=2/3,球cos(2a+π/3)的值
单独根号3不包括sin

f(x)=2sin(x+π/6)
f(a)=2sin(a+π/6)=2/3
所以
sin(a+π/6)=1/3
所以
cos(2a+π/3)
=1-2sin²(a+π/6)
=1-2×(1/9)
=7/9为什么cos(2a+π/3)=1-2sin²(a+π/6)?2倍角公式:cos2x=1-2sin²x