如何化简f(x)=sin^2θsinx+cos^2θcosx,化为f(x)=Asin(ωx+φ)+b的形式?

设m=sin²θ n=cos²θ
m+n=1
m²+n²
= (m+n)² - 2mn
= 1 - 2mn
= 1 - 2sin²θcos²θ
= 1 - 1/2 sin²(2θ)
f(x) = √(m²+n²) sin(x+φ)
= √(1- 1/2 sin²2θ) sin(x+φ)
其中,tanφ = n/m