Express the sum or difference as a product.
-$$\cos \frac { 7 x } { 2 } + \cos \frac { 5 x } { 2 }$$
A) $2 \cos 3 x \cos \frac { x } { 2 }$
B) $2 \sin 3 x \sin x$
C) $2 \sin 3 x \sin \frac { x } { 2 }$
D) $2 \cos 3 x$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the sum-to-product formula for cosine, which is $\cos A + \cos B = 2 \cos \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right)$. Applying this to the given expression, we get $2 \cos \left( \frac{7x/2 + 5x/2}{2} \right) \cos \left( \frac{7x/2 - 5x/2}{2} \right) = 2 \cos 3x \cos \frac{x}{2}$.

Express the Sum or Difference as a Product cos⁡7x2+cos⁡5x2\cos \frac { 7 x } { 2 } + \cos \frac { 5 x } { 2 }cos27x​+cos25x​

Express the Sum or Difference as a Product $\cos \frac { 7 x } { 2 } + \cos \frac { 5 x } { 2 }$