Question

函数f(θ)=sinθ/(√2+cosθ)的最大值?

Answer 1

y=sinθ/(√2+cosθ)

√2y+ycosθ=sinθ

sinθ-ycosθ=√2y

[1/√(1+y²)]·sinθ-[y/√(1+y²)]·cosθ=√2y/√(1+y²)

从而　sin(θ+φ)=√2y/√(1+y²),其中tanφ=-y

由于|sin(θ+φ)|≤1

所以|√2y/√(1+y²)|≤1

2y²≤1+y²

解得　-1≤y≤1

即最大值为1