Write the product as a sum or difference of trigonometric functions.
-$2 \cos 7 x \cos 4 x$
A) $\sin 11 x + \sin 3 x$
B) $\frac { 1 } { 2 } ( \cos 11 x + \cos 3 x )$
C) $\cos 3 x - \cos 11 x$
D) $\cos 11 x + \cos 3 x$

Question

Quizplus · Accepted Answer

The product-to-sum formula for cosine is $2 \cos A \cos B = \cos(A+B) + \cos(A-B)$. Applying this to $2 \cos 7x \cos 4x$, we get $\cos(7x + 4x) + \cos(7x - 4x) = \cos 11x + \cos 3x$.

Write the Product as a Sum or Difference of Trigonometric 2cos⁡7xcos⁡4x2 \cos 7 x \cos 4 x2cos7xcos4x

Write the Product as a Sum or Difference of Trigonometric $2 \cos 7 x \cos 4 x$