Let f(θ)=sinθ(sinθ+sin3θ),thenf(θ)
≥ 0 only when θ≥ 0
≤ 0 for all real θ
≥ 0 for all real θ
≤ 0 only when θ ≤0
Here ,f(θ)=sinθ(sinθ+sin3θ)
=sinθ(sinθ+sin3θ−4sin3θ)=4sin2θ(1−sin2θ)
4sin2θ cos2θ=(sin2θ)2 ∴ f(θ)≥ 0 for all real θ.
If f(θ)=sin2θ+sin2(θ+2π3)+sin2(θ+4π3),thenf(π15)