Use the sum-to-product formulas to rewrite the sum or difference as a product. $$\cos 12 \theta + \cos 8 \theta$$
A) $2 \sin 10 \theta \cos 2 \theta$
B) $2 \cos 10 \theta \sin 2 \theta$
C) $2 \sin 12 \theta \cos 8 \theta$
D) $2 \cos 10 \theta \cos 2 \theta$
E) $2 \sin 10 \theta \sin 2 \theta$

Question

Use the sum-to-product formulas to rewrite the sum or difference as a product.​ $$\cos 12 \theta + \cos 8 \theta$$ ​
A)​ $2 \sin 10 \theta \cos 2 \theta$
B)​ $2 \cos 10 \theta \sin 2 \theta$
C)​ $2 \sin 12 \theta \cos 8 \theta$
D)​ $2 \cos 10 \theta \cos 2 \theta$
E)​ $2 \sin 10 \theta \sin 2 \theta$

Quizplus · Accepted Answer

The sum-to-product formula for cosine is $\cos A + \cos B = 2 \cos \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)$. Applying this to $\cos 12\theta + \cos 8\theta$, we get $2 \cos \left(\frac{12\theta + 8\theta}{2}\right) \cos \left(\frac{12\theta - 8\theta}{2}\right) = 2 \cos 10\theta \cos 2\theta$.

Use the Sum-To-Product Formulas to Rewrite the Sum or Difference cos⁡12θ+cos⁡8θ\cos 12 \theta + \cos 8 \thetacos12θ+cos8θ

Use the Sum-To-Product Formulas to Rewrite the Sum or Difference $\cos 12 \theta + \cos 8 \theta$