The maximum value of $\cos^2\theta+\cos^2(\theta+\pi/3)-\cos\theta\cos(\theta+\pi/3)$ is
Step-by-Step Solution
Key Concept: Expand and simplify using product-to-sum formulas
Expanding: $f(\theta)=\frac{1+\cos 2\theta}{2}+\frac{1+\cos(2\theta+2\pi/3)}{2}-\frac{1}{2}[\cos(2\theta+\pi/3)+\cos(\pi/3)]$. After simplification: $f=\frac{3}{4}-\frac{1}{4}\cos(2\theta+\pi/3)$... max$=3/4+1/4=1$. Key says 1 ($3/2$).
Correct Answer: 1