三角函数已知函数f(x)=sin(π/6–2x)–0.5,x∈R(1)求f(x)的最小正周期T(2)证明f(x)+f(–x)=–2sinx.sinx

Question

三角函数
已知函数f(x)=sin(π/6 – 2x ) – 0.5, x∈R
(1)求f(x)的最小正周期T
(2)证明f(x)+f(– x)= –2sinx.sinx

Answer 1

f(x)=sin(π/6 – 2x ) – 0.5
T=2π/|w|=π
f(x)+f(-x)=sin(π/6 -2x ) – 0.5+sin(π/6 +2x ) – 0.5
=sin(π/6 +2x )+sin(π/6 -2x )-1
=1/2*cos2x+√3/2sin2x+1/2*cos2x-√3/2sin2x-1
=cos2x-1
=-2(sinx)^2